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A modified TOPSIS with a different ranking index
Abstract
As a tool for decision analysis, the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) attempts to choose alternative that should simultaneously have the closest distance from the positive ideal solution (PIS) and the farthest distance from the negative ideal solution (NIS). Although the ranking index of TOPSIS is reasonable, it contains a flaw. That is, this ranking index is irrespective of the weights of separations of an alternative from the PIS and the NIS. In other words, no matter what weights the decision-maker assigns to these two separations, the ranking results would not differ as if he has no preference for these two separations. This flaw will certainly limit the applicability of TOPSIS. By treating the separations of an alternative from the PIS and the NIS as a “cost” criterion and a “benefit” criterion, respectively, we reduced the original MCDM (Multi-Criteria Decision Making) problem to a new MCDM problem with these two criteria only. By proposing w − and w + as the weights of the “cost” criterion and the “benefit” criterion, respectively, we defined a new ranking index. Experimental results showed that if the number of alternatives exceeds two or if the relative importance of the two separations should be considered, the proposed ranking index would be a better choice. Finally, two numerical examples of a real-life case are given for illustration. In summary, the proposed ranking index is intelligible and intrinsically superior to the original ranking index in seeking compromised solutions.
... Preference by Similarity to Ideal Solution (TOPSIS) method could be applied because of its more intuitive and clearer logic among various MCDM methods. Although extant studies, such as Kuo [11], Dwivedi et al. [12], and Sun et al. [13], have improved the calculation of relative closeness in TOPSIS, their economic implications remain weak and unclear. Note that our decision maker-the bank-is usually loss-averse [14]. ...
... MCDM problems often involve multiple conflicting criteria, placing significant pressure on decision makers [11]. Several classic MCDM methods have been developed to address these challenges, including weighted sum model (WSM), weighted product model (WPM), simple additive weighting (SAW), analytic hierarchy process (AHP), elimination of choice translation reality (ELECTRE), and TOPSIS. ...
... Whereas methods such as WSM, WPM, SAW, and AHP assist decision makers in finding a single optimal solution, ELECTRE and TOPSIS offer the added advantage of generating a ranked list of alternatives. TOPSIS is particularly popular and widely applied due to its intuitive and clear logic [11]. Since its introduction, numerous improved versions of the TOPSIS method have been developed and employed to address various MCDM problems. ...
... The other arises from the utilization of diverse standards, including varying ranking indexes or different ranking criteria (foundations). Kuo 22 has conducted preliminary research on such issues, proposing a new ranking index and analyzing the consistency of ranking results obtained from existing TOPSIS indexes. The main focus of this paper is on the second form of rank inconsistency under different ranking criteria. ...
... The main focus of this paper is on the second form of rank inconsistency under different ranking criteria. Building upon Kuo's research, this paper introduces a spatial partition diagram to present a visual analysis for the consistency of ranking results in 22 . We also explore whether rankings resulting from relative closeness align with rankings based on the distances to PIS and NIS. ...
... When designing the ranking index, we take into account the distance from each alternative to the PIS and NIS, and their directions since they represent positive and negative indicators, respectively. Additionally, we also consider the differences between the distances of any two alternatives to the PIS and NIS, as well as the impact of these differences on the ranking, which sets our index apart from 22 and other existing TOPSIS-based methods. ...
Technique for order preference by similarity to ideal solution (TOPSIS) is a popular approach in multiple attribute decision-making. It ranks by estimating the separations between alternatives and the positive ideal solution (PIS) as well as the negative ideal solution (NIS). When setting the ranking rules, there are three limitations to the TOPSIS. First, there is controversy surrounding the addition of negative and positive indicators in the denominator of the ranking index, as these measurements represent opposite aspects. Second, the ranking index is also irrespective of the relative magnitudes of the distances from alternatives to PIS and NIS, resulting in incomparable situations. Third, the ranking results derived from the distances to PIS, the distances to NIS, and the relative closeness are inconsistent. To address these limitations, this paper first analyzes the inconsistency through a spatial partition diagram, that helps access the possible results under different indexes. Then, we define strong, weak, and no priority relationships between alternatives based on the differences in the distances to PIS and NIS, making the comparability enhanced. For further incorporating their differences in ranking, we also generate a relationship matrix based on the priority relationships from one alternative to all other alternatives, and devise a new, rational ranking index to address the non-additivity debate. Simulations and numerical example of a real-life case are conducted to demonstrate the rationality and superiority of the modified TOPSIS.
... . (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Hence, according to the crucial idea and formula (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), there is ...
... . (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) Hence, according to the crucial idea and formula (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13), there is ...
... ), then and cannot be compared. (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) Case 2: Considering the region ( ) and the region 4 , if ∈ ( ) and ∈ 4 , the following description can be obtained. ...
The criterion fuzzy concept refers to a fuzzy set that represents the decision-maker’s subjective
preference for each criterion within the universe of criteria. Addressing the challenge of ranking
all alternatives based on a given criterion fuzzy concept is a novel research direction in the
field of fuzzy multi-criteria ranking issues. This paper proposes a three-phase approach for multicriteria
ranking in fuzzy environments, which combines the criterion fuzzy concept and three-way
decision thinking. The proposed approach not only analyzes the decision-making characteristics of
all alternatives but also facilitates their ranking. During the first phase, a qualitative classification
method based on the criterion fuzzy concept and ideal solutions is defined, which divides all
alternatives into three independent decision sub-regions. During the second phase, by analyzing
the priority relationships among the alternatives within every sub-region, three local ranking rules
for alternatives are proposed to determine the ranking of alternatives in each classification region.
During the third phase, the semantic relations among three classification regions are considered
to give an overall ranking of all alternatives. Finally, combined with two existing quantitative
ranking indicators, multiple data sets are employed to verify the feasibility and superiority of the
proposed three-phase multi-criteria ranking approach.
... A Tomada de Decisão Multicritério faz parte da pesquisa operacional, voltada para o desenvolvimento de ferramentas matemáticas e computacionais que auxiliam na avaliação subjetiva de diferentes alternativas em várias situações (KUO, 2017). Esses métodos podem ser utilizados como uma abordagem eficaz para resolver problemas de classificação de criticidade. ...
... A Tomada de Decisão Multicritério é um processo de análise que considera múltiplos critérios qualitativos e quantitativos em situações do mundo real. Esse processo pode ser aplicado em contextos certos, incertos ou arriscados, com o objetivo de determinar o curso de ação, escolha, estratégia ou política mais adequada entre várias opções disponíveis (KUO, 2017). Para apoiar os tomadores de decisão na busca pela solução ideal, diversos tipos de modelos matemáticos foram desenvolvidos, incluindo modelos estatísticos, de previsão e simulação, além de algoritmos de programação matemática e heurísticos (ABIDIN; ABIDIN; DAUD, 2025). ...
Este artigo aborda o desenvolvimento de uma ferramenta computacional para apoio à tomada de decisão multicritério utilizando o método Analytic Hierarchy Process-Range (AHP-Range). O objetivo principal é analisar o AHP-Range e criar uma ferramenta em Python que simplifique sua aplicação, permitindo análises detalhadas e precisas sem a necessidade de cálculos manuais complexos, validada mediante um estudo de caso. A criação desta ferramenta traz benefícios significativos para a academia, sociedade e as organizações. Para a academia, é um recurso educacional valioso, facilitando o ensino e a aplicação de métodos de decisão multicritério. Para a sociedade, promove uma tomada de decisão mais informada e eficiente em diversos contextos, incluindo políticas públicas e gestão de recursos. Por fim, para as empresas, oferece uma solução prática para melhorar processos decisórios, aumentando a eficiência e competitividade organizacional. Como resultado, a pesquisa confirma a viabilidade do desenvolvimento da ferramenta, destacando o Python, inicialmente, como a linguagem de programação ideal devido à sua ampla difusão e capacidade de implementar os cálculos necessários de forma eficiente. Os resultados mostram que a ferramenta não só facilita o uso do método AHP-Range, mas também aprimora a capacidade dos usuários de realizar análises complexas de forma intuitiva e eficiente, pois possui uma interface amigável e funcionalidades robustas. Conclui-se que a ferramenta facilita o processo decisório, reduzindo o esforço cognitivo e melhorando a precisão das análises.
... However, the classical TOPSIS method does not consider the weights of alternatives separated from NIS and PIS when ranking the alternatives, which limits its applicability. Thus, Kuo [21] proposed an improved TOPSIS method to overcome this drawback. This section proposes a selection process utilizing the improved TOPSIS method. ...
... Step 4. Define the relative closeness coefficient [21] of alternative x i as: ...
As a novel linguistic representation tool, flexible linguistic expression (FLE) has substantial flexibility in expressing ambiguous and uncertain information from experts. However, FLEs pose the following challenges to developing information measurement and consensus mechanisms for FLEs-based multi-attribute group decision-making (MAGDM). (1) The current studies primarily use linguistic distribution approximation or triangular fuzzy numbers to measure the difference between FLEs indirectly without proposing an exact distance measure. (2) Few studies have been conducted on direct accurate consensus models incorporating adaptive consensus feedback mechanisms. To deal with these issues, the flexible linguistic ordinal Deng entropy (FLODE) is firstly proposed to measure the uncertainty of FLEs, and by combining it with linguistic scale functions, a new distance measure for FLEs is constructed, which can accurately measure the level of group consensus and the difference in pairwise FLEs. Subsequently, by integrating the defined FLODE with the classical entropy weight method, a new method for determining the experts’ personalized attribute weights is constructed, fully considering the impact of experts’ personalized attribute weights on decision-making results. Also, a new consensus model incorporating a minimum adjustment feedback mechanism and dynamic personalized attribute weights is developed, in which the feedback adjustment coefficients and personalized attribute weights are dynamically updated during the consensus reaching process (CRP). Lastly, an urban flooding risk assessment is applied to confirm the effectiveness of the proposed consensus model.
... The study uses the criteria importance via intercriteria correlation (CRITIC) approach to assigning weights for each performance indicator (Diakoulaki et al. 1995;Yalçin and Ünlü 2018). A multicriterion decision-making technique, the modified TOPSIS method, is used for ranking the general circulation models (Kuo 2017;Deng et al. 2000;Chakraborty 2022;Vassoney et al. 2021). ...
... This distance is linked to the criteria weights and should be taken into account when calculating distance. All other variables are weighed against PIS and NIS rather than directly against one another (Raju and Kumar 2014;Kuo 2017). The criteria weights in TOPSIS primarily act as conduits for bringing together criteria with varying performance. ...
Understanding how precipitation fluctuates geographically and temporally over a specific place due to climate change is critical. Generally, simulations of general circulation models (GCM) under different scenarios are downscaled to the local scale to study the impact of climate change on precipitation. However, selecting suitable GCMs for the given study area is one of the most hectic tasks, as the performance of GCMs may vary with respect to space and timescale. Therefore, the current study ranks twenty-seven CMIP 6 (Coupled Modelled Intercomparison Project Phase 6) GCMs in simulating precipitation over India for nine times series, including daily, monthly, yearly, and six extreme series extracted with annual maximum and peak over threshold methods. The gridded daily rainfall data provided by the India Meteorological Department (IMD) are used as the observed data. The GCMs' outputs are corrected for the systematic bias using the linear scaling method. The performance of a GCM is assessed with three statistical performance metrics, namely NSE, RMSE, and R2. The GCMs' ranks are determined using a multi-criterion decision-making technique named the modified technique of order preference by similarity to an ideal solution (mTOPSIS) for every grid point and nine timescales (i.e., daily, monthly, yearly, and six extreme series). From the results, for the entire India, the top ten recommended CMIP 6 GCMs are FGOALS-g3, HadGEM3-GC31-MM, EC-Earth3, BCC-CSM2-MR, CNRM-CM6-1-HR, CanESM5, AWI-ESM-1-1-LR, MPI-ESM-1-2-HR, IITM-ESM, and INM-CM5-0. The identified best-performing models provide insightful information for better regional climate projections and underscore the necessity of considering multiple model outputs for reliable climate change impact assessments and adaptation strategies in the region.
... This technique provides several solution alternatives by ordering criteria based on Euclidean distances. The order of the criteria created according to distance is the minimum distance to the positive ideal solution and the maximum distance to the negative ideal solution [83,84]. Thus, comparing positive and negative ideal solutions yields optimal results [85]. ...
... The studies carried out in [30,32,34,96,104] used just the AHP approach. There are also numerous studies that use only the VIKOR [19,[105][106][107] and TOPSIS [21,84,86,87] methods. There have been few studies combining multiple approaches. ...
The indiscriminate use of surface water has heightened the demand for groundwater supplies. Therefore, it is critical to locate potential groundwater sources to develop alternative water resources. Groundwater detection is tremendously valuable, as is sustainable groundwater management. Mersin, in southern Türkiye, is expected to confront drought shortly due to increased population, industry, and global climate change. The groundwater potential zones of Mersin were determined in this study by GIS-based AHP, VIKOR, and TOPSIS methods. Fifteen parameters were used for this goal. The study area was separated into five categories. The results show that the study area can be divided into “Very High” zones (4.98%, 5.94%, 7.96%), followed by “High” zones (10.89%, 10.32%, 16.50%), “Moderate” zones (60.68%, 52.41%, 51.56%), “Low” zones (21.28%, 28.53%, 20.90%), and “Very Low” zones (2.18%, 2.80%, 3.07%) in turn. Data from 60 wells were used to validate potential groundwater resources. The ROC-AUC technique was utilized for this. It was seen that the performance of the VIKOR model is better than that of the AHP and TOPSIS (76.5%). The findings demonstrated that the methods and parameters used are reliable for sustainable groundwater management. We believe that the study will also help decision makers for this purpose.
... The best choice is the alternative closest to the PIS and furthest from the NIS. The TOPSIS method is easy to understand, simple to compute, and has solved many different problems [47,48]. The concept of aspiration level is introduced in this study as TOPSIS-AL. ...
... The closeness coefficient (CC p ) is proposed by Kuo [48], which improves many shortcomings of conventional TOPSIS to obtain more reliable ranking results, as shown in Equation (22). The new ranking index has a better judgment basis, with the value range of CC p ranging from −1 to 1 and the sum of CC p being 0. ...
Fitness influencers are an emerging profession in recent years. At present, the main research on fitness influencers focuses on their personal traits, professional knowledge and skills, and course content, while there is still a large research gap on the social media marketing strategies of fitness influencers, how they interact with fans, and the reasons for their influence on fans. There is a lack of a comprehensive evaluation framework for fitness influencer research, and there is no clear research on what competencies are required to become a qualified fitness influencer. Therefore, it has become an important issue to establish a comprehensive fitness influencer competency evaluation. In this study, a hybrid model of fitness influencer competency evaluation framework was developed based on government competency standards and expert knowledge using the Multiple Criteria Decision-Making (MCDM) model perspective. This evaluation should expand to include the principles of sustainable development, emphasizing the influencers’ role in advocating for environmental responsibility, social equity, and economic viability within the fitness industry. First, the study developed 21 criteria in six dimensions of fitness influencer competencies through a literature survey and interviews with several experts. The 21 criteria resonate with many of the Sustainable Development Goals (SDGs), including SDG 3 (Good Health and Well-being), SDG 4 (Quality Education), SDG 5 (Gender Equality), SDG 10 (Reduced Inequalities), and SDG 11 (Sustainable Cities and Communities). The Bayesian Best-Worst Method (Bayesian BWM) was used to generate the best group weights for fitness influencer competencies. Then, a modified Technique for Order Preference by Similarity to the Ideal Solution Based on Aspiration Level (modified TOPSIS-AL) was applied to evaluate the performance ranking of major fitness influencers in Taiwan by integrating the concept of the aspiration level. The results of the study revealed that behavioral standards were the most important dimension, emphasizing the need for fitness influencers to establish a comprehensive set of norms for their own behavioral standards. The top five criteria for fitness influencers’ competencies were self-review, punctuality and prudence, creativity, rapport and motivation, and the need to conform to one’s body image. The performance ranking was used to compare the evaluated subjects to the desired level to obtain a basis for improvement. This study effectively identifies key fitness industry competency indicators and refines business performance through the management implications proposed in this study to facilitate the development of the fitness industry.
... Considering multiple risk factors, the priority order of FMs is the aim of FMEA. In this connection, many approaches have been proposed, such as the TOPSIS-based approach [21], VIKRO-based approach [48], TODIM-based approach [16], TODIM-ELECTRE II-based approach [25], gained and lost dominance score (GLDS)-based approach [27,28], ORESTE-based method [32,38], ELICIT-ORESTE-based approach [13], behavioral TOPSIS-based approach [7] etc. The comparative studies in [27] proved the superiority of the GLDS-based ranking approach regarding the handling of stereotactic body radiation therapy cases for lung cancer. ...
... (5) The purpose of FMEA is to prioritize likely failure modes so that appropriate precautions may be taken. In this connection, many proposals were given [7,13,16,21,25,27,28,32,38,48]. In this paper, we improve the GLDS-based ranking method [27,28,40] based on the degree of similar proximity of experts' opinions on the object under the LZN environment for risk prioritization. ...
Most of the cancer patients cannot get the usual treatment in the advanced stage of the disease. In particular, for breast cancer, it is to use a special kind of radiation that targets the tumour while the patient holds their breath. This is called surface-guided (SG) breast radiotherapy (RT) with deep inspiration breath-hold (DIBH). This treatment is very complicated and different from the normal way of treating breast cancer. It can also have many errors and problems that are not well-studied or understood. To prevent these problems, we need to use a method called failure mode and effects analysis (FMEA). This method helps us find and rank the possible risks and how to avoid them. In keeping with this aim, this paper studies consensus-reaching process-based group decision-making (GDM) with completely unknown risk factors' weights and the gained-lost dominance score (GLDS)-based ranking process. We cannot avoid the uncertainty related to relativity information in medical science. Therefore, in this study, we offer the experts to provide their opinions using the linguistic Z number (LZN) because LZN is designed to capture such types of information in medical science. For the consensus-reaching process (CRP), the relativity among experts is considered for consensus measurement, and the minimum adjustment sum with group consensus opinion-based feedback is offered. For unknown weight of risk factors, we don't know how much each risk factor weighs. So, we use a method that combines two ways of calculating weights. One way is a subjective weight computation process, and the other way is based on the data using entropy and division. Finally, we applied our proposed CRP-based GDM approach for ranking the identified failure modes related to the SG DIBH RT process. We conduct sensitive, comparative, and statistical assessments to ensure our method is reasonable and practical.
... There are very many different aspects of TOPSIS that have so far been addressed and described. Among them, there are assorted adaptations of the method [11,12], issues with the method, e.g. the so-called rank-reversal problem [13,14], and numerous TOPSIS applications [15][16][17]. Therefore the following brief list of TOPSISrelated papers will be confined to those papers that describe selected methodological adaptations of TOPSIS, in particular its extensions and generalizations. ...
TOPSIS, a popular method for ranking alternatives, is based on aggregated distances to ideal and anti-ideal points. As such, it was considered to be essentially different from widely popular and acknowledged ’utility-based methods’, which build rankings from weight-averaged utility values. Nonetheless, TOPSIS has recently been shown to be a natural generalization of these ’utility-based methods’ on the grounds that the distances it uses can be decomposed into so-called weight-scaled means (WM) and weight-scaled standard deviations (WSD) of utilities. However, the influence that these two components exert on the final ranking cannot be in any way implemented in the standard TOPSIS. This is why, building on our previous results, in this paper we put forward modifications that make TOPSIS aggregations responsive to WM and WSD, achieving some amount of well interpretable control over how the rankings are influenced by WM and WSD. The modifications constitute a natural generalization of the standard TOPSIS method because, thanks to them, the generalized TOPSIS may turn into the original TOPSIS or, otherwise, following the decision-maker’s preferences, may trade off WM for WSD or WSD for WM. In the latter case, TOPSIS gradually reduces to a regular ’utility-based method’. All in all, we believe that the proposed generalizations constitute an interesting practical tool for influencing the ranking by controlled application of a new form of decision-maker’s preferences.
... There are very many different aspects of TOPSIS that have so far been addressed and described. Among them, there are assorted adaptations of the method ( [11,12]), issues with the method, e.g. the so-called rank-reversal problem ( [13,14]), and numerous TOPSIS applications ( [15][16][17]). Therefore the following brief list of TOPSISrelated papers will be confined to those papers that describe selected methodological adaptations of TOPSIS, in particular its extensions and generalizations. ...
TOPSIS, a popular method for ranking alternatives is based on aggregated distances to ideal and anti-ideal points. As such, it was considered to be essentially different from widely popular and acknowledged `utility-based methods', which build rankings from weight-averaged utility values. Nonetheless, TOPSIS has recently been shown to be a natural generalization of these `utility-based methods' on the grounds that the distances it uses can be decomposed into so called weight-scaled means (WM) and weight-scaled standard deviations (WSD) of utilities. However, the influence that these two components exert on the final ranking cannot be in any way influenced in the standard TOPSIS. This is why, building on our previous results, in this paper we put forward modifications that make TOPSIS aggregations responsive to WM and WSD, achieving some amount of well interpretable control over how the rankings are influenced by WM and WSD. The modifications constitute a natural generalization of the standard TOPSIS method because, thanks to them, the generalized TOPSIS may turn into the original TOPSIS or, otherwise, following the decision maker's preferences, may trade off WM for WSD or WSD for WM. In the latter case, TOPSIS gradually reduces to a regular `utility-based method'. All in all, we believe that the proposed generalizations constitute an interesting practical tool for influencing the ranking by controlled application of a new form of decision maker's preferences.
... The TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method, a key component of MCDA, ranks alternatives by comparing their distance to an ideal solution [10]. This technique identifies the best option as the one closest to the positive ideal (most desirable) and furthest from the negative ideal (least desirable). ...
Large language models (LLMs) hold the potential to significantly enhance data annotation for free-text healthcare records. However, ensuring their accuracy and reliability is critical, especially in clinical research applications requiring the extraction of patient characteristics. This study introduces a novel evaluation framework based on Multi-Criteria Decision Analysis (MCDA) and the Order of Preference by Similarity to Ideal Solution (TOPSIS) technique, designed to benchmark LLMs on their annotation quality. The framework defines ten evaluation metrics across key criteria such as age, gender, BMI, disease presence, and blood markers (e.g., white blood count and platelets). Using this methodology, we assessed leading open source and commercial LLMs, achieving accuracy scores of 0.59, 1, 0.84, 0.56, and 0.92, respectively, for the specified criteria. Our work not only provides a rigorous framework for evaluating LLM capabilities in healthcare data annotation but also highlights their current performance limitations and strengths. By offering a comprehensive benchmarking approach, we aim to support responsible adoption and decision-making in healthcare applications.
... This study seeks to introduce a method for EV drivers to assess and help ranking the nearby charging stations based on different common preferences at their current location. The goal of this study is to apply the best-worst method (BWM) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to assist electric vehicle drivers in identifying the most suitable charging stations (Kuo, 2017;Rezaei, 2015). This research study has been structured in the following arrangement. ...
... The fundamental principle of TOPSIS is to select the option that is farthest distant from the negative ideal solution (NIS) and closest to the positive ideal solution (PIS) (Kuo, 2017). For each criterion, the NIS denotes the worst possible values, and the PIS the best. ...
Implementing Multiple Criteria Decision Making (MCDM) methodologies into marketing mix procedures provides a disciplined way of dealing with complicated decision-making situations. This study investigates the use of MCDM approaches such as the Analytic Hierarchy Process (AHP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), and Multi-Attribute Utility Theory (MAUT) to optimise the 4Ps-Product, Price, Place, and Promotion. Businesses may use these approaches to evaluate and prioritise alternative marketing tactics depending on customer preferences, market trends, and financial restrictions. The study explores the transformation of traditional 4P to 4A's in confluence with 4C's. It demonstrates how MCDM provides a robust framework for balancing trade-offs, improving decision accuracy, and aligning marketing tactics with corporate goals. Based on the analysis, MCDM technologies may help marketers make better awareness and data-driven decisions, resulting in increased competitiveness and market success.
... The most common methods used in the summarized studies were Weighted overlay Analysis, AHP, and Fuzzy Logic. Studies that solely utilized AHP include [1], [18], Fuzzy [20], and TOPSIS [21]. While few studies used combined methods [22]. ...
The maintenance of ecological diversity, public health, and economic expansion depends on appropriately managing groundwater supplies. This study focuses on the Markanda Watershed, a region characterized by its diverse topography, and pressing issues such as groundwater over-extraction, seasonal water shortages, and flooding. The analytic hierarchy process (AHP) and fuzzy AHP are two highly developed techniques and scientific ideas used in this work to discover groundwater potential zones (GWPZs). The GWPZs are determined employing 12 thematic layers. Using both approaches, these thematic maps are weighted based on their characteristics and water potential. Upon analysis with the AHP and Fuzzy-AHP, four zones – low 0.034% (0.0124 km2) and 13.535278% (4.8727 km2), moderate 44.59% (16.0532 km2) and, 37.17% (13.3812 km2), high 52.923% (19.0523 km2) and 42.2575% (15.21217 km2) and very high 2.450% (0.8821 km2) and 7.0372222% (2.5334 km2) were revealed in this study that indicate different levels of groundwater potential. Validation through Receiver Operating Characteristics (ROC) analysis indicates that the Fuzzy-AHP model achieves an accuracy of 76.3%, compared to 71.43% for the AHP model. Based on the study’s findings, a targeted groundwater management plan is proposed to optimize resource use and sustainability. High-potential zones should be prioritized for groundwater extraction and recharge. Moderate-potential areas require a balanced approach. Low-potential zones should focus on reducing groundwater dependence and enhancing surface water storage to prevent overexploitation. These strategies aim to ensure sustainable groundwater management, promote ecological balance, and support socio-economic development.
... In addition to the developments above, Kuo (2017) investigated weighting on the elements of the TOPSIS ranking index, showing that the proposed modified ranking index outperforms the traditional TOPSIS in ranking consistency. Mufazzal and Muzakkir (2018) proposed a proximity index to overcome RR, utilizing Manhattan distance to count separation measures and using the sum of distances as the ranking index. ...
This paper examines ranking reversal (RR) in Multiple Criteria Decision Making (MCDM) using the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). Through a mathematical analysis of min-max and max normalization techniques and distance metrics (Euclidean, Manhattan, and Chebyshev), the study explores their impact on RR, particularly when new, high-performing alternatives are introduced. This research provides insight into the causes of RR, offering a framework that clarifies when and why RR occurs. The findings help decision-makers select appropriate techniques, promoting more consistent and reliable outcomes in real-world MCDM applications.
... This new ranking index was proposed by Kuo [16], who treated the separations of an alternative from the PIS and the NIS as a "cost" criterion and a "benefit" criterion, respectively. The parameter θ denotes the importance of the "cost "criterion and 1 − θ denotes the "benefit "criterion. ...
The aim of this paper is to provide a specific numerical scale model with the purpose of making transformations between linguistic terms and numerical values. The proposed method represents a wide range of existing numerical scale models and can quantitatively reflect the linguistic behaviors of DMs. The pessimistic-optimistic principle based supplementary regulation for hesitant fuzzy linguistic term set (HFLTS) may lead to the initial information distortion and losing. On the basis of the lowest common multiple principle in number theory, an improved supplementary regulation is proposed to reserve the fidelity of original information, the improved supplementary regulation brings a new conception for information measures of HFLTS as well. Then based on the traditional generalized distance and Hausdorff distance measures, some new distance measures for HFLTS are presented in the numerical scale framework. Furthermore, an extended TOPSIS method for hesitant fuzzy linguistic MADM is developed. Finally, a numerical example concerning the preference of movies is elaborated on the performance of our approach. Sensitive and comparative analysis are also provided and discussed to show the effectiveness and advantages of the proposed method
... The TOPSIS method is a mathematical framework used to measure the sustainability performance of different alternatives and rank them by coupling LCSA data with the criteria weights [34][35][36][37]. Backes et al. [27] demonstrate that the integration of the LCSA and TOPSIS methods applied in the construction sector has been explored less than AHP. ...
... TOPSIS consists of five different steps (Kuo, 2017), which are outlined below. The first step involves the standardization of the data. ...
Purpose
The measurement of regional competitiveness is becoming essential for policymakers to address territorial disparities, while considering the issue of correlations among indicators. Therefore, the purpose of this paper is to measure regional competitiveness using the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) by considering different distance measures and two levels of analysis to provide a comparative and comprehensive measurement of regional competitiveness in Europe.
Design/methodology/approach
The authors apply TOPSIS based on three different distance measures (the Manhattan, the Euclidean and the Mahalanobis distance measures) to the regions of the EU Regional Competitiveness Index (RCI) 2019, which is taken as the frame of reference.
Findings
The authors replicate the RCI by using TOPSIS with a less preferred choice of distance measure, indicating TOPSIS as a valuable method for policymakers in the analysis of regional competitiveness. The authors argue in favour of the Mahalanobis distance measure as the best of the three, as it considers correlations among macro-economic indicators.
Originality/value
This study aims to make three contributions. Firstly, by replicating the RCI by means of TOPSIS with a less preferred choice of distance measure, the paper provides a benchmark for future research on regional competitiveness. Secondly, by suggesting the use of TOPSIS with the use of the Mahalanobis distance measure, the authors show how to measure regional competitiveness by taking into account correlations among pillars. Thirdly, the authors argue in favour of considering clusters of regions when measuring regional competitiveness.
... TOPSIS'i uygulamak için, bir dizi kriter üzerinden bir dizi alternatif için karar matrisinin spesifikasyonuna ve ayrıca bu kriterler için göreceli ağırlıklar setinin spesifikasyonuna ihtiyaç bulunmaktadır (Kuo, 2017). TOPSIS yönteminin uygulama adımları şu şekilde sıralanabilir: ...
Amaç: Bu araştırmada Bazı Avrupa Birliği ülkelerinin (Bulgaristan, Danimarka, Finlandiya, Fransa, Almanya, Macaristan, Yunanistan, Portekiz, Polonya, İtalya, Romanya, İspanya, Litvanya) tarımsal yapılarının incelenmesi amaçlanmıştır. Çalışmada kullanılan değişkenler, tarım alanı, ekilebilir arazi, toplam istihdam içinde tarımın payı, tarım orman ve balıkçılıktan elde edilen katma değer ve ekilebilir arazi başına gübre tüketimidir. Materyal ve Yöntem: Araştırmanın verileri 2021 yılına aittir. Avrupa Birliği ülkelerinin tarımsal yapılarının karşılaştırılmasında TOPSIS yöntemi kullanılmıştır. Araştırma Bulguları: Araştırmada ele alınan kriterler itibariyle tarımsal potansiyeli en yüksek Avrupa Birliği ülkeleri Fransa, İspanya ve Almanya iken en düşük ülkeler, Litvanya, Danimarka ve Finlandiya olarak bulunmuştur. Sonuç: Araştırmada Avrupa Birliği ülkelerinin tarımsal yapıları arasında önemli farklılıkların olduğu belirlenmiştir. Ülkeler arasındaki söz konusu farklılıkların giderilmesi için gerekli tedbirler alınmalıdır.
... Currently, there is a dearth of systematic studies addressing product structure issues from a green design perspective. In response, this paper integrates the entropy weight-TOPSIS and PSO-SVR methods [42] at the early stage of new product development to determine the optimal product design portfolio based on key emotions (KEs). By taking NEVs as the research subject, dimensionality reduction in factor analysis (FA) yields four representative perceptual words: modern, green, energetic, and elegant. ...
With the growing emphasis on eco-friendly and sustainable development concepts, new energy vehicles (NEVs) have emerged as a popular alternative to traditional fuel vehicles (FVs). Due to the absence of an internal combustion engine, electric vehicles (EVs) do not require a front air intake grille, allowing for a more minimalist and flexible design. Consequently, aligning EV styling with users’ visual cognition and emotional perception is a critical objective for automakers and designers. In this study, we establish the mapping relationship between users’ emotional cognition and NEV styling design based on experimental data. We introduce Particle Swarm Optimization Support Vector Regression (PSO-SVR) into the perceptual engineering (KE) research process to predict user emotions using Support Vector Regression (SVR). To optimize the three hyperparameters (penalty coefficient C, RBF kernel function parameter γ, and insensitivity loss coefficient ε) of the SVR model, we utilize the Particle Swarm Optimization (PSO) algorithm. The results indicate that the proposed PSO-SVR model outperforms traditional SVR and BPNN models in predicting NEV user emotions. This model effectively captures the nonlinear relationship between battery electric vehicle (BEV) morphological features and users’ emotional cognition, providing a novel method for enhancing NEV design. The results of this research are expected to drive design innovation and technological advancement in the new energy vehicle industry, contributing to the achievement of the ambitious goal of global eco-friendliness and sustainable development.
... The FTOPSIS method, initially developed by Hwang andYoon in 1981 (Kumar et al., 2017) aims to ascertain the disparities between favorable and unfavorable strategies by establishing positive and negative gaps (Kuo, 2017). This method assists in the selection of options that not only have the shortest distance from the positive ideal solution but also exhibit the greatest separation from the negative ideal solution (Vinodh et al., 2014). ...
Purpose-The construction industry in developed countries is witnessing a paradigm shift towards modular construction methods, driven by the need for efficiency, sustainability, and cost-effectiveness. However, the realization of these benefits in the context of developing countries is hindered by numerous barriers. Against this backdrop, this study seeks to contribute insights into the barriers hindering the adoption of modular construction in developing countries, specifically Nigeria, and further formulate effective strategies.
Design/methodology/approach-A thorough review of existing literature was conducted to identify the multifaceted barriers hindering the adoption of modular construction and the corresponding strategies. Subsequently, a panel of 13 experts were invited to utilize the Fuzzy Analytic Hierarchy Process (FAHP) approach to systematically evaluate these barriers based on their impact. Furthermore, the experts implored the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach to select and prioritize the most suitable strategies to mitigate these barriers.
Findings-The study revealed that the most critical barriers to modular construction are Client resistance to change and innovation, Limited experience in module installation, and Transportation constraints. Additionally, the study prioritizes 13 strategies, with the Development of effective guidelines, standards, and policies ranked highest. The insights from the ranking using the FAHP and TOPSIS approach were adopted to develop a framework for modular implementation in developing countries.
Research limitations/implications-This study is limited to Nigeria due to its status as the country with the highest Gross Domestic Product (GDP) in Africa, and it is considered a suitable representation of the region as most of the countries in Africa are categorized as developing nations.
Practical implications-By highlighting the most critical barriers and prioritizing effective strategies, the study provides actionable insights for overcoming obstacles to modular construction adoption. Decision-makers can use this information to develop targeted policies and training programs to promote the adoption of modular construction in developing countries.
Originality/value-The research provides valuable insights by not only identifying critical barriers but also presenting prioritized strategies, distinguishing itself from previous studies, and establishing itself as a novel resource for developing countries. This adopt a novel hybrid MCDM approach for modular construction in developing countries such as Nigeria which can serve as reference point to other developing countries seeking to adopt modular construction and leverage its numerous benefits.
... A comparison between TOPSIS and Modified TOPSIS is made by [20] using simulation and mathematical analysis. To reduce the complexity of the original MCDM problem, [21] developed a new ranking index by assigning different weights to the criteria "cost" and "benefit." Additionally, [22] Kuo [22] presented an improved fuzzy semantics-dependent plagiarism detection scheme for analyzing and matching texts using the WordNet lexical dataset. ...
Detecting plagiarism poses a significant challenge for academic institutions, research centers, and content-centric organizations, especially in cases involving subtle paraphrasing and content manipulation where conventional methods often prove inadequate. Our paper proposes FTLM (Fuzzy TOPSIS Language Modeling), a novel method for detecting plagiarism within decision science. FTLM integrates language models with fuzzy sorting techniques to assess plagiarism severity by evaluating the similarity of potential solutions to a reference. The method involves two stages: leveraging language modeling to define criteria and alternatives and implementing enhanced fuzzy TOPSIS. Word usage patterns, grammatical structures, and semantic coherence represent fuzzy membership functions. Moreover, pre-trained language models enhance semantic similarity analysis. This approach highlights the benefits of combining fuzzy logic’s tolerance for imprecision with the semantic evaluation capabilities of advanced language models, thereby offering a comprehensive and contextually aware method for analyzing plagiarism severity. The experimental results on the benchmark dataset demonstrate effective features that enhance performance on the user-defined severity ranking order.
... Subsequently, a "condition of satisfiability" is presented for each criterion, succeeded by a maximum-minimum operator for these criteria. The resolution of overlapping usages is achieved by implementing Harmony, as highlighted in a previous study [21]. Among the efficient methodologies is TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution), designed for optimal solution-like regulatory performance. ...
High-performance parallel computing involves the simultaneous execution of multiple tasks or processes, orchestrated to achieve improved computational speed and efficiency. This approach leverages the power of parallelism, exploiting both multi-core CPUs and GPUs, distributed computing clusters and specialized hardware accelerators. The fundamental idea is to divide a task into smaller sub-tasks that can be executed concurrently, thereby reducing processing time and enhancing overall performance. High performance parallel computing is a transformative approach that enables us to tackle computationally intensive tasks efficiently. This abstract highlight its significance in contemporary computing and sets the stage for further exploration of the intricacies and innovations within this dynamic field. Researchers and practitioners continue to push the boundaries of what is achievable, making high-performance parallel computing a cornerstone of modern computational science and technology. High-performance parallel computing research is of paramount significance due to its transformative impact across diverse fields. It empowers scientists to tackle complex problems that were once computationally intractable, unlocking new frontiers in scientific discovery. It drives innovation in engineering and design, optimizing product development and manufacturing processes across industries. In healthcare, it accelerates genomics
research and drug discovery, offering hope for improved medical treatments. Financial institutions rely on it for data analysis and risk assessment, shaping the global economy. Weather forecasting and environmental modelling are enhanced, aiding disaster preparedness and conservation efforts. In the digital age, parallel computing underpins artificial intelligence, enabling advancements in natural
language processing and machine learning. Furthermore, it has vital applications in national security, space exploration and materials science. In essence, high-performance parallel computing research serves as the backbone of technological progress, fostering innovation, efficiency and problem-solving across a wide spectrum of disciplines, ultimately shaping the future of our world. TOPSIS method
involves evaluating the geometric distance between each alternative solution and two reference solutions: the positive ideal solution and the negative ideal solution. The underlying principle of TOPSIS assumes that the criteria being assessed are of an ascending nature, where larger values represent better performance. To account for disparate dimensions or scales among the criteria, normalization is often
employed within the TOPSIS framework.
... TOPSIS, there are doubts about its efficacy due to several reasons. One criticism is the neglect of the relative importance of different sections, which can lead to issues, particularly when dealing with multiple goals in Multi-Objective Decision Making (MODM) [22]. To address this, TOPSIS can be modified by incorporating the satisfaction levels for each criterion, determined through the max-min operator This enhances the technique's effectiveness in analyzing and comparing options. ...
Asia's largest stock market, Indian stock market holds a pivotal position in the country's economy. Operating primarily through it is deeply influenced by government policies, global economic trends, corporate performance, and investor sentiment. These factors collectively shape the dynamics of the Indian economy as reflected in the market. Despite periodic fluctuations, the market has witnessed significant growth over the years, attracting both domestic and international investors. It offers diverse investment opportunities across various sectors such as technology, finance, pharmaceuticals, and manufacturing. Regulatory bodies like maintaining transparency and fairness in market procedures. the Indian stock market, conducting research holds significant importance. It serves as the cornerstone for making well-informed decisions, providing insights into market trends, company performance, and economic indicators. Thorough research empowers investors to identify profitable opportunities, mitigate risks, and enhance the long-term growth potential of their portfolios. Moreover, it facilitates understanding and compliance with regulatory changes and market dynamics, enabling investors to stay ahead of the curve. Essentially, research empowers investors in the Indian stock market, instilling confidence, minimizing risks, and maximizing opportunities. The TOPSIS ranking system, augmented with weighted averages and ambiguity comparisons, is commonly utilized. One approach involves addressing uncertainties to diminish ambiguity and adjusting both the weight and character of responses simultaneously. In TOPSIS, multiple responses are employed to adopt a holistic global perspective Mutual Funds, Exchange-Traded Funds (ETFs), Real Estate Investment Trusts (REITs), Gold and Precious Metals, Direct Equity Investments, Derivatives, Fixed Income Instruments, Portfolio Management Services (PMS) and Cryptocurrencies. Market Indices, Risk Management and Investor Sentiment. the Ranking of the Indian Stock Market. Direct Equity Investments got the first rank whereas the Real Estate Investment Trusts (REITs) have the Lowest rank.
... Comparing with Topsis, the results can be analyzed. M Tapsis has found the approach very suitable, and the analysis involves determining attribute weights for E-topsis, referred to as tapsis or U-Topsis [23]. This examination revolves around the TOPSIS ranking index, which is essentially a ranking criterion. ...
Explainable Artificial Intelligence (XAI) refers to the development of AI systems are transparent, explainable and their comprehensible for results can provide explanations or predictions. As AI technologies, particularly machine learning models, become more complex and sophisticated, there is a
growing need to ensure that their decisions can be comprehended and trusted by humans, especially health,
Finance and such as criminal justice in important domains. Evaluating Explainable Artificial Intelligence (XAI) is essential to ensure transparency, accountability, and user trust in AI systems. Interpretability is a key factor examining how easily the model's internal mechanisms can be understood. Model transparency,
feature importance and the clarity of visualizations contribute to this aspect. Differentiate between posthoc and intrinsic explanations considering whether the model inherently provides interpretable insights. The distinction between local and global explanations is crucial, as it determines whether explanations
focus on individual predictions or the overall model behavior. Robustness and consistency are assessed through stability and sensitivity analysis ensuring that explanations remain reliable across similar instances. Additionally, ethical considerations such as fairness and transparency in decision-making must be addressed to uncover and mitigate biases. User feedback and the relevance of explanations to the specific use case contribute to a comprehensive evaluation, fostering the development of XAI systems that are not only technically robust but also ethically sound and user-friendly. The significance of research in
Explainable Artificial Intelligence (XAI) lies in addressing critical challenges associated with the adoption and deployment of AI systems in various domains. As AI technologies, particularly complex machine learning models become integral to decision-making processes in areas such as healthcare, finance and
criminal justice, the need for transparency and interpretability becomes paramount. TOPSIS involves optimizing from an advantageous standpoint by simultaneously minimizing the distance to and maximizing the distance from a reference point, which is defined in relation to solutions within a set of alternative
options and numerous identification criteria. The importance of TOPSIS criteria lies in the potential to integrate comparative weights. This study conducts a comprehensive review of TOPSIS, exploring various weighing schemes and employing different distance measurements. Numerous applications of TOPSIS are
examined particularly its utilization in comparing results for a diverse set of multiple criteria data with varying weights. Interpretable Machine Learning Models, Human-Centric Design in XAI, Ethical Implications of XAI, Industry-specific Applications of XAI and Hybrid Approaches for Model Interpretability, Interpretability Metrics, Human-Subjective Evaluation, Algorithmic Robustness and real world impacts, Impact the Ranking of Evaluation of Explainable Artificial Intelligence. Industry-specific applications of XAI ranked high while the ethical Implications of XAI are ranked low.
... It is especially useful when making decisions under conditions of ambiguity or imprecision. The TOPSIS technique enables decision-makers to take into consideration trade-offs and conflicts among various criteria by taking into account both positive and negative criteria [31][32][33][34][35][36][37][38]. Some other decision making methods can be surveyed from [39][40][41][42]. ...
Fuzzy set theory is a mathematical method for dealing with uncertainty and imprecision in decision-making. Some of the challenges and complexities involved in medical diagnosis can be addressed with the help of fuzzy set theory. Ovarian cancer is a disease that affects the female reproductive system's ovaries, which also make the hormones progesterone and estrogen. The ovarian cancer stages demonstrate how far the disease has spread from the ovaries to other organs. The TOPSIS technique (Technique for Order Preference by Similarity to Ideal Solution) aids in selecting the best option from a selection of choices by taking into account a number of variables. It provides a ranking or preference order after weighing the benefits and drawbacks of each solution. Intuitionistic fuzzy soft set (IFSS) is the framework to deal with the uncertain information with the help of the parameters. The goal of this article is to develop some basic aggregation operators (AOs) based on the IFSS and then use them to diagnose the stages of the ovarian cancer using the TOPSIS technique. Furthermore, the variation of the parameters used in the developed model AOs is also observed and graphically represented.
... Tapsis technique(Walczak, D. and Rutkowska, A. (۲۰۱۷)),(Aryanpour,A. and Veysanloo,F. and Asgari,M.(۲۰۱٤)),(Kuo, T.(2017)) ...
Every year, a significant portion of the country's credits and financial resources are allocated to investment in civil and infrastructural projects. Risk management can prevent cost escalation and assist in completing projects within the designated time and budget. This study aims to identify factors contributing to the lack of implementation of risk management in small-scale civil projects in the city of Abadan. The research utilizes a descriptive method for data collection and employs exploratory factor analysis and TOPSIS analytical methods to identify and prioritize the factors. The results indicate that the influential factors in the lack of implementing risk management include four main elements (technical risk barriers, project management and leadership obstacles, construction risk barriers, financial risk barriers), among which the option of insufficient knowledge of the contractor has priority over other options.
... TOPSIS has been widely applied in performance evaluation problems, such as sustainable cities and communities assessment [49], green low-carbon port evaluation [50], software requirements selection [51]. This study integrated Pythagorean fuzzy sets with TOPSIS, and enhanced practicality of TOPSIS by the new ranking index proposed by Kuo [52], is leveraged to achieve a more accurate ranking. The steps for PF-TOPSIS are outlined as follows: ...
As the complexity and uncertainty of global supply chains escalate, disruptions have become an increasingly common challenge in supply chain management. Suppliers, who serve as essential connectors for the seamless movement of goods and materials critical to production and distribution, are often at the center of these disruptions, highlighting their significant impact on the overall stability of the supply chain. This study proposes an innovative approach to assessing supplier disruption risks by combining the Pythagorean Fuzzy Step-wise Weight Assessment Ratio Analysis (PF-SWARA) with the Pythagorean Fuzzy Technique for Order Preference by Similarity to Ideal Solution (PF-TOPSIS). By reviewing the literature and consulting with supply chain experts, eight key risk factors were identified. The PF-SWARA method then quantifies the significance of these risks, while a modified PF-TOPSIS technique calculates each supplier’s risk score, facilitating the prioritization of suppliers for targeted improvement. The findings of the study indicate that “natural disasters and geopolitical risks,” “financial instability,” and “delivery delays” emerge as the top three critical disruption risk factors. Suppliers facing higher disruption risks should, therefore, formulate improvement strategies that target these three areas.
... It can be carried with the help of TOPSIS as it is one of the popular techniques for material selection under multi-attribute decision making environment. The TOPSIS procedure includes various steps such as the formulation of decision matrix, normalizing the decision matrix, establishment of weighted normalized decision matrix, determining positive ideal solution (PIS) and negative ideal solution (NIS), calculation of separation measures and closeness coefficient (Ci) for each alternative [20,21].The weightages of MCs obtained through Eq. (1) are utilized to establish weighted normalized decision matrix for determining closeness coefficient (Ci) of all the materials. The materials could be ranked in accordance with the values of Ci for all the materials. ...
... The selection process of TOPSIS can be explained in terms of two extreme reference points (PIS and NIS) for a sequence containing n points, which is to find the solution with the minimum distance from PIS and the maximum distance from NIS as the optimal solution and the second most suboptimal. In recent years, many researchers [28][29][30][31] have promoted and improved the TOPSIS method. However, these methods can only be said to be extensions of the TOPSIS method, and only achieve the purpose of optimizing the decision results. ...
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a method for ranking a limited number of alternatives based on their closeness to an idealized goal. For specific decision-making problems, there may be some alternatives whose merits cannot be judged. Many researchers have proposed some improved ranking methods that enable a more accurate ranking result of the alternatives. However, these methods only serve to rank the alternatives, not to classify them. In order to extend the application scope and decision-making ability of TOPSIS method, this paper designs a three-way TOPSIS method that can handle both classification and ranking of alternatives by introducing sequential three-way decisions. Specifically, we first use the basic principles of TOPSIS method to obtain the Positive Ideal Solution (PIS) and Negative Ideal Solution (NIS) of the alternatives, and design four different three-way TOPSIS models are designed according to the distance measures of each alternative to different ideal solutions. Then we employ sequential three-way decision to divide the alternatives in order to obtain the corresponding decision regions. The alternatives are initially ranked according to the ranking rules of the same decision region, and the final ranking is performed using the ranking rules of different decision regions. Finally, this paper verifies the validity and feasibility of the method through an example about project investment to test the results and comparative analysis.
... Since it has a strong mathematical basis, is straightforward to use, and is simple, TOPSIS has been extensively applied to real-world MCDM issues (Yeh, 2003). It has inspired several innovations in methods and comparative analyzes (Kuo, 2017;Zavadskas, Mardani, Turskis, Jusoh, & Nor, 2016). TOPSIS assumes that the optimum answer is the one that is closest to the positive-ideal option and the one that is farthest away from the negative-ideal option. ...
We have proposed a data-driven method for spatio-temporal analysis of car crashes based on the Multi Criteria Decision Making (MCDM) procedure in the Zanjan city, NW Iran which are recorded in the period 2019-2020. A combination of Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is used in this paper to accurately identify the spatio-temporal interactions exist in car crashes. A data-driven AHP-TOPSIS procedure is arranged based on assigning proper weights to the time series related to the peak of accidents. On the other hand, for spatial analysis, the Kernel Density Estimation method was used to create the continuous-value maps of different traffic accidents and then classified using Natural Breaks Classifier. In fact, the proposed methodology can be used to identify car crash hotspots by considering spatio-temporal interactions as well as addressing exaggerated weightings arising from knowledge-driven modeling. By using the spatio-temporal interaction maps in which the location and time of crashes are considered, simultaneously, it is possible to provide a new scientific strategy for identifying car crash hotspots which can lead to better traffic management, improved allocation of resources, and enhanced prevention regulations.
Nesta pesquisa, o objetivo central é a classificação da criticidade dos processos auditáveis em uma empresa do setor portuário no Rio de Janeiro. Em paralelo, é apresentada uma nova abordagem para o Apoio Multicritério à Decisão (AMD), fundamentada no método Analytic Hierarchy Process (AHP). O diferencial desta abordagem, intitulada Analytic Hierarchy Process-Range (AHP-Range), reside na eliminação da necessidade do decisor na avaliação de pesos e relevância dos critérios ao comparar alternativas preferíveis. A metodologia adotada incorpora a amplitude como parte essencial do AHP-Range, assemelhando-se ao Analytic Hierarchy Process Gaussian (AHP-Gaussian). Ambos pertencem ao grupo de métodos compensatórios, nos quais os critérios são considerados independentes, e critérios qualitativos precisam ser convertidos em valores quantitativos. No que tange aos ganhos e descobertas, a aplicação do estudo de caso proporciona benefícios variáveis, dada a adaptabilidade da problemática a diferentes organizações e situações de tomada de decisão. Além disso, do ponto de vista acadêmico, a contribuição se direciona à comunidade de Pesquisa Operacional e à sociedade em geral, oferecendo uma perspectiva inovadora para tomadas de decisão multicritério, com ênfase na ordenação de alternativas. A fim de validar os resultados, foi realizada a análise comparativa dos resultados do estudo de caso entre os métodos AHP-Gaussian e AHP-Range, no qual revelou uma ordenação consistente e estável, consolidando a eficácia da nova abordagem proposta, mediante a análise de sensibilidade.
Purpose
This study aims to focus on sustainable supplier selection in a construction company considering a new multi-criteria decision-making (MCDM) method based on dominance-based rough set analysis. The inclusion of sustainability concept in industrial supply chains has started gaining momentum due to increased environmental protection awareness and social obligations. The selection of sustainable suppliers marks the first step toward accomplishing this objective. The problem of selecting the right suppliers fulfilling the sustainable requirements is a major MCDM problem since various conflicting factors are underplay in the selection process. The decision-makers are often confronted with inconsistent situations forcing them to make imprecise and vague decisions.
Design/methodology/approach
This paper presents a new method based on dominance-based rough sets for the selection of right suppliers based on sustainable performance criteria relying on the triple bottom line approach. The method applied has its distinct advantages by providing more transparency in dealing with the preference information provided by the decision-makers and is thus found to be more intuitive and appealing as a performance measurement tool.
Findings
The technique is easy to apply using “jrank” software package and devises results in the form of decision rules and ranking that further assist the decision-makers in making an informed decision that increases credibility in the decision-making process.
Originality/value
The novelty of this study of its kind is that uses the dominance-based rough set approach for a sustainable supplier selection process.
Battery electric vehicles are an evolution in the automobile industry as they also contribute to reducing the harmful effects of vehicles on the environment because of fossil fuels and the release of carbon dioxide. The purchasing decision of the consumer is highly dependent on the specific criteria when it comes to the adoption of Battery electric vehicles. This work helps to analyze those specific criteria that are important from a consumer point of view before purchasing a BEV. The selected criteria analyzed in this study are the range of the vehicle, its full charging time, the purchasing price of the vehicle, the battery capacity of the vehicle, and the energy consumption of the vehicle. The analysis to find out the most prominent criteria that affect the purchasing decision of the consumer is done with the help of the Fuzzy AHP approach which provides the weights of the selected criteria and the other technique used is the Technique for Order Preference by Similarity to Ideal Solution TOPSIS, which provides the rank of the selected alternative electric vehicles.
Multi-criteria decision making is a complex process that involves considering various criteria or factors when making a decision. Over the past few decades, several researchers have developed different methods to tackle this problem. This method offers manifold advantages, however, it faces several limits leading to the development of different modified forms. This paper provides a comprehensive review on the TOPSIS concept to help the researchers gain an overview in different aspects of TOPSIS. The literature review presented in this paper offers a comprehensive survey of the TOPSIS method, providing researchers with an overview of the various aspects of the method, its strengths and limitations, and its various applications. The results of the literature review also are provided based on the application, methodology, and reasons to use TOPSIS method.
Targeting the shortcomings of low round-trip efficiency (RTE) in unitized regeneration proton exchange membrane fuel cell (UR-PEMFC), a model incorporated combined cooling, heating, and power (CCHP) technology for UR-PEMFC was proposed, which integrated a three-dimensional two-phase flow field model with a zero-dimensional system model. Additionally, a multi-criterion evaluation system was introduced for the URFC-CCHP system, which encompasses three decision-making methods. To illustrate the applicability of the model, the assessments of four typical flow field configurations were utilized as case studies and presented their rankings. The results reveal that, compared to a system focused on electrical power output, the system exhibited a remarkable enhancement in RTE, increasing from 35.96 % to 76.67 %. Notably, during the cold season, the RTE surpassed that of the warm season by 8.74 %–10.62 %. Operating under a cyclic condition of fast charging and slow discharging proved to be conducive to maintaining the optimal RTE of the system. Furthermore, the computational outcomes of the three decision-making methods in the multi-criterion evaluation system exhibited consistency, unanimously identifying the optimal flow field as the three-serpentine flow field, while designating the single-serpentine flow field as the least favorable. It aims to present a novel technology for enhancing the RTE of UR-PEMFC.
The node importance evaluation of internet of drones also called unmanned aerial vehicle swarm network can assist network administrators in implementing security protection for important nodes. Slow down attacks on important nodes, and providing support for network enhancement. Complex network is a strong theoretical tool in modeling, analysing, and identifying the most important drone nodes. Most researchers utilize single attribute of nodes, such as degree, betweenness centrality, and so on, to perform node importance assessment. However, the methods involved either only consider the local features of nodes or only concentrate on the nodes' participation on the shortest path. Aiming at this problem, we develop a three-way decisions based Pythagorean fuzzy TOPSIS model. It selects multiple measures of nodes as attributes to assess node importance. Additionally, it considers the Pythagorean fuzzy middle ideal solution that induced by new proposed Pythagorean fuzzy operator. Simulation results manifest its feasibility in assessing node importance.
Multicriteria decision-making (MCDM) is an important branch of operations research which composes multiple-criteria to make decision. TOPSIS is an effective method in handling MCDM problem, while there still exist some shortcomings about it. Upon facing the MCDM problem, various types of uncertainty are inevitable such as incompleteness, fuzziness, and imprecision result from the powerlessness of human beings subjective judgment. However, the TOPSIS method cannot adequately deal with these types of uncertainties. In this paper, a D -TOPSIS method is proposed for MCDM problem based on a new effective and feasible representation of uncertain information, called D numbers. The D -TOPSIS method is an extension of the classical TOPSIS method. Within the proposed method, D numbers theory denotes the decision matrix given by experts considering the interrelation of multicriteria. An application about human resources selection, which essentially is a multicriteria decision-making problem, is conducted to demonstrate the effectiveness of the proposed D -TOPSIS method.
To satisfy the demand for higher data rate while maintaining the quality of service, a dense long-term evolution (LTE) cells environment is required. This imposes a big challenge to the network when it comes to performing handover (HO). Cell selection has an important influence on network performance, to achieve seamless handover. Although a successful handover is accomplished, it might be to a wrong cell when the selected cell is not an optimal one in terms of signal quality and bandwidth. This may cause significant interference with other cells, handover failure (HOF), or handover ping-pong (HOPP), consequently degrading the cell throughput. To address this issue, we propose a multiple-criteria decision-making method. In this method, we use an integrated fuzzy technique for order preference by using similarity to ideal solution (TOPSIS) on S-criterion, availability of resource blocks (RBs), and uplink signal-to-interference-plus-noise ratio. The conventional cell selection in LTE is based on S-criterion, which is inadequate since it only relies on downlink signal quality. A novel method called fuzzy multiple-criteria cell selection (FMCCS) is proposed in this paper. FMCCS considers RBs utilization and user equipment uplink condition in addition to S-criterion. System analysis demonstrates that FMCCS managed to reduce handover ping-pong and handover failure significantly. This improvement stems from the highly reliable cell-selection technique that leads to increased throughput of the cell with a successful handover. The simulation results show that FMCCS outperforms the conventional and cell selection scheme (CSS) methods.
Inter-dependency among the decision criteria and difficulty of establishing a common membership grade are two important issues to be addressed in multi-criteria group decision making (MCGDM) problems in the environment of uncertainty. The main purpose of this paper is to define the Choquet integral operator for interval-valued intuitionistic hesitant fuzzy sets (IVIHFS) and to extend the technique for order preference by similarity to ideal solution (TOPSIS) method using Choquet integral operator in interval-valued intuitionistic hesitant fuzzy environment. In the present study we define interval-valued intuitionistic hesitant fuzzy Choquet integral (IVIHFCI) operator and extend the definition of hamming distance for the elements of IVIHFS. Using IVIHFCI operator and hamming distance for IVIHFS, we extend TOPSIS method for MCGDM for interval-valued intuitionistic hesitant fuzzy environment considering the interaction phenomena among the decision criteria. An illustrative example has also been taken in the present study to understand the proposed method.
The TOPSIS method is a technique for establishing order preference by similarity to the ideal solution, and was primarily developed for dealing with real-valued data. This technique is currently one of most popular methods for Multiple Criteria Decision Making (MCDM). In many cases, it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values. A number of papers have been devoted to fuzzy extensions of the TOPSIS method in the literature, but these extensions are not complete since the ideal solutions are usually presented as real values (not by fuzzy values) or as fuzzy values which are not attainable in the decision matrix. In most of these papers, a defuzzification of elements of the fuzzy decision matrix is used, which leads inevitably to a loss of important information and may even produce the wrong results. In this paper, we propose a new direct approach to the fuzzy extension of the TOPSIS method which is free of the limitations of other known approaches. We show that the distances of the alternatives from the ideal solutions may be treated (in some sense) as modified weighted sums of local criteria. It is known that using weighted sums is not the best approach to the aggregation of local criteria in many real-world situations. Therefore, here, we propose the use, in addition to weighted sums, some other types of local criteria aggregation in the TOPSIS method and we develop a method for the generalization of different aggregation modes, providing compromised final results.
Multicriterion Decision-Making (MCDM) can be perceived as a process of evaluating real-world situations based on various qualitative/quantitative criteria in certain/uncertain/risky environments in order to find a suitable course of action/choice/strategy/policy among the several available options.
This book concentrates on the basic principles of multicriterion analysis and acquaints the reader with the recent trends in MCDM analysis. It explains the basics of Structured Decision-Making (SDM) and describes the various features of traditional optimization methods such as linear and non-linear programming, and dynamic programming, as well as non-traditional optimization methods such as genetic algorithms, differential evolution, and simulated annealing and quenching.
The text elaborates the normalization methods, weight estimation methods and multiobjective optimization methods both in traditional and non-traditional environments. Classification approaches with cluster validation indices, discrete MCDM methods both in deterministic and fuzzy approach and group decision-making methods are discussed in detail. Advanced topics in decision-making such as data envelopment analysis, Taguchi methodology, ant colony optimization, and particle swarm optimization are also covered.
In addition, the book includes many case studies for better comprehension of the procedures involved in the methods.
KEY FEATURES :
Introduces relevant software to keep the students updated and aware of its potentiality and applicability in multicriterion analysis.
Includes a summary at the end of each chapter to facilitate quick revision of the key learning points.
Provides a number of solved problems to enable students to acquire a clear understanding of the concepts and methods discussed.
Offers several problems at the end of each chapter with answers to help students develop problem-solving skills.
PowerPoint presentations for each chapter are available for instructors.
This book is designed for undergraduate and postgraduate courses in operations research, optimization, soft computing, fuzzy logic and other related courses in engineering and management programmes. It will also be useful to researchers and professionals working in the fields of operations research and management studies.
Decision making in construction management has been always complicated especially if there were more than one criterion under consideration. Multiple criteria decision making (MCDM) has been often applied for complex decisions in construction when a lot of criteria were involved. Traditional MCDM methods, however, operate with independent and conflicting criteria. While in every day problems a decision maker often faces interactive and interrelated criteria. Accordingly, the need of improving and supplementing the methodology of compromise decisions arose. It was proposed to supplement TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution) method and integrate the Mahalanobis distance in the usual algorythm of TOPSIS. Mahalanobis distance measure offered an option to take the correlations between the criteria into considerations while making the decision. A case study of building redevelopment in Lithuanian rural areas was presented that demonstrated the application of the proposed methodology. The case study proved that the proposed TOPSIS‐M (TOPSIS applying Mahalanobis distance measure) method could have substantial influence in carrying the proper decision.
Santrauka
Statybos valdymo spendimų priėmimas visuomet yra komplikuotas, ypač jei turime atsižvelgti į daugelį rodiklių. Kompleksiniams statybos sprendimams, kurie apibūdinami daugeliu rodiklių, taikomi daugiatiksliai sprendimų priėmimo metodai (MCDM ‐ Multiple Criteria Decision Making). Šie metodai skirti sprendimams priimti tuomet, kai vertinami konfliktuojantys bei nepriklausomi rodikliai. Tačiau realiose situacijose, priešingai, nuolat susiduriame su saveikaujančiais ir tarpusavio priklausomybę turinčiais rodikliais. Dėl šios priežasties kyla poreikis patobulinti sprendimų metodologiją. Straipsnyje siūloma papildyti variantų racionalumo nustatymo metoda TOPSIS (Technique for the Order Preference by Similarity to Ideal Solution), taikant Mahalanobio metoda atstumams nustatyti. Mahalanobio atstumų nustatymo metodas suteikia galimybę įvertinti koreliacinės rodiklių priklausomybės priimant daugiatikslį sprendimą. Siūlomos metodologijos taikymas įliustruojamas sprendžiant apleistų pastatų Lietuvos kaimo vietovėse racionalaus sutvarkymo uždavinį. Pateiktas pavyzdys patvirtina, kad TOPSIS‐M metodo (t. y. TOPSIS naudojant Mahalanobio atstuma) taikymas gali turėti esminę įtaka priimant sprendimą.
First published online: 21 Oct 2010
Reikšminiai žodžiai: statybos valdymas, MCDM, TOPSIS, TOPSIS‐M, rodikliai, koreliacija, kovariacija, Euklido atstumas, Mahalanobio atstumas
The paper presents risk assessment of construction projects. The assessment is based on the multi‐attribute decision‐making methods. The risk evaluation attributes are selected taking into consideration the interests and goals of the stakeholders as well as factors that have influence on the construction process efficiency and real estate value. Ranking of objects and determination of their optimality are determined by applying TOPSIS grey and COPRAS‐G methods with attributes values determined at intervals. A background and a description of the proposed model are provided and key findings of the analysis are presented.
Santrauka
Straipsnyje vertinama statybos projektu rizika. Vertinimas pagristas ivairiais daugiatikslio vertinimo metodais. Rizikos vertinimo rodikliai atrenkami, atsižvelgiant i suinteresuotu šaliu interesus, tikslus ir veiksnius, kurie turi itakos statybos proceso efektyvumui ir nekilnojamojo turto vertes didinimui. Projektai surikiuoti pagal naudinguma, nustatyti santykiniai ju optimalumo dydžiai. Uždavinio modeliui aprašyti ir jam išspresti taikomi TOPSIS grey ir COPRAS‐G metodai. Projektu savybes aprašomos efektyvumo rodikliu reikšmemis, apibrežiamomis intervaluose. Straipsnyje aprašomas taikomas modelis, atlikta uždavinio analize ir pateikiamos trumpos išvados.
First Published Online: 14 Oct 2010
Reikšminiai žodžiai: sprendimu priemimas, statyba, rizika, ivertinimas, rodikliai, TOPSIS grey, COPRAS‐G, rangavimas
Simultaneous consideration of multiple financial ratios is required to adequately evaluate and rank the relative performance of competing companies. This paper formulates the inter-company comparison process as a multi-criteria analysis model, and presents an effective approach by modifying TOPSIS for solving the problem. The modified TOPSIS approach can identify the relevance of the financial ratios to the evaluation result, and indicate the performance difference between companies on each financial ratio. To ensure that the evaluation result is not affected by the inter-dependence of the financial ratios, objective weights are used. As a result, the comparison process is conducted on a commonly accepted basis and is independent of subjective preferences of various stakeholders. An empirical study of a real case in China is conducted to illustrate how the approach is used for the inter-company comparison problem. The result shows that the approach can reflect the decision information emitted by the financial ratios used. The comparison of objective weighting methods suggests that, with the modified TOPSIS approach, the entropy measure compares favourably with other methods for the case study conducted.
Decision makers are often faced with several conflicting alternatives. How do they evaluate trade-offs when there are more than three criteria? To help people make optimal decisions, scholars in the discipline of multiple criteria decision making (MCDM) continue to develop new methods for structuring preferences and determining the correct relative weights for criteria. A compilation of modern decision-making techniques, Multiple Attribute Decision Making: Methods and Applications focuses on the fuzzy set approach to multiple attribute decision making (MADM). Drawing on their experience, the authors bring together current methods and real-life applications of MADM techniques for decision analysis. They also propose a novel hybrid MADM model that combines DEMATEL and analytic network process (ANP) with VIKOR procedures. The first part of the book focuses on the theory of each method and includes examples that can be calculated without a computer, providing a complete understanding of the procedures. Methods include the analytic hierarchy process (AHP), ANP, simple additive weighting method, ELECTRE, PROMETHEE, the gray relational model, fuzzy integral technique, rough sets, and the structural model. Integrating theory and practice, the second part of the book illustrates how methods can be used to solve real-world MADM problems. Applications covered in the book include: • AHP to select planning and design services for a construction project • TOPSIS and VIKOR to evaluate the best alternative-fuel vehicles for urban areas • ELECTRE to solve network design problems in urban transportation planning • PROMETEE to set priorities for the development of new energy systems, from solar thermal to hydrogen energy • Fuzzy integrals to evaluate enterprise intranet web sites • Rough sets to make decisions in insurance marketing Helping readers understand how to apply MADM techniques to their decision making, this book is suitable for undergraduate and graduate students as well as practitioners.
The rapid evolution in mobile wireless communication networks has generated Heterogeneous Wireless Networks (HWNs), which cover a diverse range of networks (e.g., 2G, 3G, and LTE-A). In HWNs, a mobile device supports multiple network interfaces that use different access methods for wireless links. In such an environment, the main challenge is Always Best Connected (ABC), which means that the mobile nodes rank the network interfaces and select the best one at anytime and anywhere according to multiple criteria (application-related criteria, network-related criteria, terminal-related criteria, user-related criteria). In this context, Multi Attribute Decision Making (MADM) techniques present a promising solution for the network interface selection problem. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one widely adopted MADM method. TOPSIS suffers from ranking abnormalities, e.g., if a low-ranking network (alternative) is disconnected or a new network is discovered, then the order of the higher-ranking networks will change abnormally. These abnormalities can potentially decrease the quality of the results. In this paper, we propose new TOPSIS-based approaches for network interface selection that efficiently tackle the ranking abnormality problem in HWNs. The performance of our methods is evaluated through simulations. The results show that the proposed approaches reduce or completely eliminate the rank reversal, either when networks are disconnected or new networks are connected.
Multiple criteria decision-making (MCDM) is a difficult task because the existing alternatives are frequently in conflict with each other. This study presents a hybrid MCDM method combining simple additive weighting (SAW), techniques for order preference by similarity to an ideal solution (TOPSIS) and grey relational analysis (GRA) techniques. A feature of this method is that it employs an experimental design technique to assign attribute weights and then combines different MCDM evaluation methods to construct the hybrid decision-making model. This model can guide a decision maker in making a reasonable judgment without requiring professional skills or extensive experience. The ranking results agreed upon by multiple MCDM methods are more trustworthy than those generated by a single MCDM method. The proposed method is illustrated in a practical application scenario involving an IC packaging company. Four additional numerical examples are provided to demonstrate the applicability of the proposed method. In all of the cases, the results obtained using the proposed method were highly similar to those derived by previous studies, thus proving the validity and capability of this method to solve real-life MCDM problems.
This paper proposes a new multiple criteria decision-making method called ERVD (election based on relative value distances). The s-shape value function is adopted to replace the expected utility function to describe the risk-averse and risk-seeking behavior of decision makers. Comparisons and experiments contrasting with the TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution) method are carried out to verify the feasibility of using the proposed method to represent the decision makers’ preference in the decision making process. Our experimental results show that the proposed approach is an appropriate and effective MCDM method.
Identifying influential nodes in complex networks is still an open issue. Although various centrality measures have been proposed to address this problem, such as degree, betweenness, and closeness centralities, they all have some limitations. Recently, technique for order performance by similarity to ideal solution (TOPSIS), as a tradeoff between the existing metrics, has been proposed to rank nodes effectively and efficiently. It regards the centrality measures as the multi-attribute of the complex network and connects the multi-attribute to synthesize the evaluation of node importance of each node. However, each attribute plays an equally important part in this method, which is not reasonable. In this paper, we improve the method to ranking the node's spreading ability. A new method, named as weighted technique for order performance by similarity to ideal solution (weighted TOPSIS) is proposed. In our method, we not only consider different centrality measures as the multi-attribute to the network, but also propose a new algorithm to calculate the weight of each attribute. To evaluate the performance of our method, we use the Susceptible-Infected-Recovered (SIR) model to do the simulation on four real networks. The experiments on four real networks show that the proposed method can rank the spreading ability of nodes more accurately than the original method.
In order to compete in the global environment, a manufacturing company has to keep developing new technologies. Selection of a right technology is a critical stage in a successful technology transfer process. However, technology selection is a complex multi-dimensional problem including both qualitative and quantitative factors, such as human resources, operational and financial dimensions, which may be in conflict and may also be uncertain. In addition, interdependent relationships exist among various dimensions as well as criteria of technology selection. The identified problems could be solved by combining multiple criteria decision making (MCDM) methods of different nature and fuzzy set theory. The objective of the current paper is to develop a complex approach to evaluate technologies and to rank their appropriateness for a company. A hybrid model is proposed, based on Fuzzy Analytic Network Process (FANP) and Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS). A real-life case study is presented to validate the proposed model.
In this paper, financial performance of Taiwan container shipping companies are evaluated by fuzzy multi-criteria decision-making (FMCDM). In the evaluating problem, we first apply grey relation analysis to partition financial ratios into several clusters and find representative indices from the clusters. Then the representative indices are considered as evaluation criteria on financial performance assessment of Taiwan container shipping companies, and an FMCDM method called fuzzy technique for order preference by similarity to ideal solution (fuzzy TOPSIS) is utilized to evaluate financial performance. By fuzzy TOPSIS, financial performances of container shipping companies are ranked, and thus a container shipping company can realize its finance competitive strength and weakness between container shipping companies.
Selection of an optimum decision depends on two types of measures: (1) the efficiency of a course of action for an outcome; (2) the importance or weight of the outcomes. That course of action that maximizes the expected total weighted efficiency (effectiveness) is optimum. A method for estimating importance on a scale of value is provided. It is based on actual or verbal choices of decision-makers. The method can be applied to any number of objectives or outcomes, and to any number of decision-makers. Reliability of the results can be measured.
Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application.
The problem of machine tool selection among available alternatives has been critical issue for most companies in fast-growing markets for a long time. In the presence of many alternatives and selection criteria, the problem becomes a multiple-criteria decision making (MCDM) machine tool selection problem. Therefore, most companies have utilized various methods to successfully carry out this difficult and time-consuming process. In this work, both of the most used MCDM methods, the modified TOPSIS and the Analytical Network Process (ANP) are introduced to present a performance analysis on machine tool selection problem. The ANP method is used to determine the relative weights of a set of the evaluation criteria, as the modified TOPSIS method is utilized to rank competing machine tool alternatives in terms of their overall performance. Furthermore, in this paper, we use a fuzzy extension of ANP, a more general form of AHP, which uses uncertain human preferences as input information in the decision-making process, because AHP cannot accommodate the variety of interactions, dependencies and feedback between higher and lower level elements. Instead of using the classical eigenvector prioritization method in AHP, only employed in the prioritization stage of ANP, a fuzzy logic method providing more accuracy on judgments is applied. The resulting fuzzy ANP enhances the potential of the conventional ANP for dealing with imprecise and uncertain human comparison judgments. The proposed approach is also applied for a real-life case in a company.
One of the challenging and famous types of MCDM (Multiple Criteria Decision Making) problems that includes both quantitative and qualitative criteria is Facility location selection problem. For the common fuzzy MCDM problems (Type-1 fuzzy MCDM problems), the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the common fuzzy numbers. However, in the majority of cases, determining the exact membership degree for each element of the fuzzy sets which are considered for the ratings of alternatives with respect to the criteria or/and the values of criteria weights as a number in interval [0,1], is difficult. In this situation, the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the IVFNs (Interval Valued Fuzzy Numbers) and thereby the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be used. In this paper, the authors propose an IVF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method based on uncertainty risk reduction in decision making process. By using this method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The proposed method is also compared with another IVF-TOPSIS method. As a result, the authors concluded that in addition to benefits such as simplicity and ease of use that exist in the previous IVF-TOPSIS methods, the proposed method has a significant reliability and flexibility and is practical for facility location selection problems and other IVF-MCDM problems.
The technique for order preference by similarity to ideal solution (TOPSIS) method is a well-known compromising method for multiple criteria decision analysis. This paper develops an extended TOPSIS method with an inclusion comparison approach for addressing multiple criteria group decision-making problems in the framework of interval-valued intuitionistic fuzzy sets. Considering the relative agreement degrees and the importance weights of multiple decision makers, this paper presents a modified hybrid averaging method with an inclusion-based ordered weighted averaging operation for forming a collective decision environment. Based on the main structure of the TOPSIS method, this paper utilizes the concept of inclusion comparison possibilities to propose a new index for an inclusion-based closeness coefficient for ranking the alternatives. Additionally, two optimization models are established to determine the criterion weights for addressing situations in which the preference information is completely unknown or incompletely known. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a medical group decision-making problem.
Green product development has become a key strategic consideration for many companies due to regulatory requirements and the public awareness of environmental protection. Life cycle assessment (LCA) is a popular tool to measure the environmental impact of new product development. Nevertheless, it is often difficult to conduct a traditional LCA at the design phase due to uncertain and/or unknown data. This research adopts the concept of LCA and introduces a comprehensive method that integrates Fuzzy Extent Analysis and Fuzzy TOPSIS for the assessment of environmental performance with respect to different product designs. Methodologically, it exhibits the superiority of the hierarchical structure and the easiness of TOPSIS implementation whilst capturing the vagueness of uncertainty. A case study concerning a consumer electronic product was presented, and data collected through a questionnaire survey were used for the design evaluation. The approach presented in this research is expected to help companies decrease development lead time by screening out poor design options.
Nowadays, it is imperative need for the State to support Small Medium Enterprises (SMEs) operation in this difficult business environment through the development and adoption of appropriate policies, fostering green entrepreneurship and green energy growth. This paper aims to present a coherent and transparent methodological multi-criteria framework, using linguistic variables, for assessing companies' energy and environmental corporate policies. The use of linguistic variables is a realistic approach, taking into consideration that the information needed is often unquantifiable, imprecise and uncertain. The proposed framework is based on the developed 2-tuple TOPSIS method, with its application to a number of SMEs. Moreover, a comparison with the 2-tuple LOWA operator and a sensitivity analysis are provided. According to the results, SMEs that integrate systematic environmental practices, beyond the required legislation, achieve high overall performance. These SMEs come mainly from countries with essential implementation of Corporate Social Responsibility (CSR) concepts.
The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.
Accuracy, complexity and interpretability are very important in credit classification. However, most approaches cannot perform well in all the three aspects simultaneously. The objective of this study is to put forward a classification approach named C-TOPSIS that can balance the three aspects well. C-TOPSIS is based on the rationale of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution). TOPSIS is famous for reliable evaluation results and quick computing process and it is easy to understand and use. However, it is a ranking approach and three challenges have to be faced for modifying TOPSIS into a classification approach. C-TOPSIS works out three strategies to overcome the challenges and retains the advantages of TOPSIS. So C-TOPSIS is deduced to have reliable classification results, high computational efficiency and ease of use and understanding. Our findings in the experiment verify the advantages of C-TOPSIS. In comparison with 7 popular approaches on 2 widely used UCI credit datasets, C-TOPSIS ranks 2nd in accuracy, 1st in complexity and is in 1st rank in interpretability. Only C-TOPSIS ranks among the top 3 in all the three aspects, which verifies that C-TOPSIS can balance accuracy, complexity and interpretability well.
In complex networks, identifying influential nodes is the very important part of reliability analysis, which has been a key issue in analyzing the structural organization of a network. In this paper, a new evaluation method of node importance in complex networks based on technique for order performance by similarity to ideal solution (TOPSIS) approach is proposed. TOPSIS as a multiple attribute decision making (MADM) technique has been an important branch of decision making since then. In addition, TOPSIS is first applied to identify influential nodes in a complex network in this open issue. In different types of networks in which the information goes by different ways, we consider several different centrality measures as the multi-attribute of complex network in TOPSIS application. TOPSIS is utilized to aggregate the multi-attribute to obtain the evaluation of node importance of each node. It is not limited to only one centrality measure, but considers different centrality measures, because every centrality measure has its own disadvantage and limitation. Then, we use the Susceptible–Infected (SI) model to evaluate the performance. Numerical examples are given to show the efficiency and practicability of the proposed method.
Evaluation of the competitiveness of high-tech industry is a technical decision-making issue involving multiple criteria. It is also a practical path to promote a country’s competitiveness. However, the competitiveness indicators in high-tech industry often act and react upon one another. Moreover, different dimensions and indicator weights also affect the evaluation results. In this paper, the Mahalanobis distance is used to improve the traditional technique for order preference by similarity to ideal solution (TOPSIS). The improved TOPSIS method has the following properties: (1) an improved relative closeness which is invariant after non-singular linear transformation, and (2) the weighted Mahalanobis distance is the same as the weighted Euclidean distance when the indicators are uncorrelated. The new method is applied to evaluate the competitiveness of the Chinese high-tech industry using data from 2011. Consideration of the correlation between indicators improves the evaluation results (in terms of sorting and closeness) to a certain extent compared to the traditional TOPSIS method. The top five provinces are: Guangdong, Jiangsu, Shanghai, Beijing, and Shandong. This finding reflects the practical linkage among provinces and softens the closeness value, consistent with reality.
Due to an increased awareness and significant environmental pressures from various stakeholders, companies have begun to realize the significance of incorporating green practices into their daily activities. This paper proposes a framework using Fuzzy TOPSIS to select green suppliers for a Brazilian electronics company; our framework is built on the criteria of green supply chain management (GSCM) practices. An empirical analysis is made, and the data are collected from a set of 12 available suppliers. We use a fuzzy TOPSIS approach to rank the suppliers, and the results of the proposed framework are compared with the ranks obtained by both the geometric mean and the graded mean methods of fuzzy TOPSIS methodology. Then a Spearman rank correlation coefficient is used to find the statistical difference between the ranks obtained by the three methods. Finally, a sensitivity analysis has been performed to examine the influence of the preferences given by the decision makers for the chosen GSCM practices on the selection of green suppliers. Results indicate that the four dominant criteria are Commitment of senior management to GSCM; Product designs that reduce, reuse, recycle, or reclaim materials, components, or energy; Compliance with legal environmental requirements and auditing programs; and Product designs that avoid or reduce toxic or hazardous material use.
Electronic government (E-government) readiness assessment is a relatively new concept that has been given impetus by the rapid rate of Internet penetration and advances in information and communication technologies (ICT). Over the years, various e-government readiness assessment methods have been proposed by different organizations. These methods use a wide range of indicators to assess a community's e-government readiness. However, most of these methods suffer from poor data quality and fragmented measurement efforts. In this paper, we propose a hybrid fuzzy model, based on the group Analytic Network Process (ANP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), to assess a community's overall e-government readiness from a Citizen Relationship Management (CiRM) perspective. For practitioners, we present the results of a pilot study to demonstrate the complexities inherent in e-government readiness assessment.
The TOPSIS method is a technique for order preference by similarity to ideal solution. This technique currently is one of the most popular methods for Multiple Criteria Decision Making (MCDM). The TOPSIS method was primary developed for dealing with only real-valued data. In many cases, it is hard to present precisely the exact ratings of alternatives with respect to local criteria and as a result these ratings are considered as intervals. There are some papers devoted to the interval extensions of TOPSIS method, but these extensions are based on different heuristic approaches to definition of positive and negative ideal solutions. These ideal solutions are presented by real values or intervals, which are not attainable in a decision matrix. Since this is in contradiction with basics of classical TOPSIS method, in this paper we propose a new direct approach to interval extension of TOPSIS method which is free of heuristic assumptions and limitations of known methods. Using numerical examples we show that “direct interval extension of TOPSIS method” may provide the final ranking of alternatives which is substantially different from the results obtained using known methods.
Many authors have investigated multiattribute decision making (MADM) problems under interval-valued intuitionistic fuzzy sets (IVIFSs) environment. This paper presents an optimization model to determine attribute weights for MADM problems with incomplete weight information of criteria under IVIFSs environment. In this method, a series of mathematical programming models based on cross-entropy are constructed and eventually transformed into a single mathematical programming model to determine the weights of attributes. In addition, an extended technique for order preference by similarity to ideal solution (TOPSIS) is suggested to ranking all the alternatives. Furthermore, an illustrative example is provided to compare the proposed approach with existing methods. Finally, the paper concludes with suggestions for future research.
Project portfolio managers are multi-objective Decision-Makers (DMs) who are expected to select the best mix of projects by maximizing profits and minimizing risks over a multiperiod planning horizon. However, project portfolio decisions are complex multi-objective problems with a high number of projects from which a subset has to be chosen subject to various constraints and a multitude of priorities and preferences. We propose a Goal Programming (GP) approach for project portfolio selection that embraces conflicting fuzzy
goals with imprecise priorities. A fuzzy goal with an aspiration level and a predefined membership function is defined for each objective. The impreciseness in the priorities of the membership values of the fuzzy goals is modeled with fuzzy relations. This leads to type II fuzzy sets since fuzzy relations are organized between the membership values of the fuzzy goals which are themselves fuzzy sets. The proposed model is based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and fuzzy preference relations. TOPSIS is used to reduce the multi-objective problem into a bi-objective problem. The resulting bi-objective problem is solved with fuzzy GP (FGP). The fuzzy preference relations are used to help DMs express their preferences with respect to the membership values of the fuzzy goals. The proposed approach is used to solve a real-life problem characterized as a fuzzy Multi-Objective Project Selection with Multi-Period Planning Horizon (MOPS–MPPH). The performance of the proposed approach is compared with a competing method in the literature. We show that our approach generates high-quality solutions with minimal computational efforts.
1. Introduction. 2. SMART, direct rating. 3. The AHP, pairwise comparisons. 4. Scale sensitivity and rank preservation. 5. The alternatives in perspective. 6. Group decision making. 7. Resource allocation. 8. Scenario analysis. 9. Conflict analysis and negotiations. 10. Multi-objective linear programming. 11. MCDA in the hands of its masters. 12. Prospects of MCDA. Subject index. About the author.
A description and evaluation is made of several existing methods designed to help decision-makers deal with the multiple-decision problem. In all types of decision situations, the alternatives from which a choice must be made are characterized by multiple attributes (or properties). As the number of relevant attributes and alternatives increases, the ability of the decisionmaker to handle the problem decreases, and the information-processing requirements may rapidly exceed the decisionmaker's processing capacity. Methods to deal with this problem include Dominance, Satisficing, Maximin, Minimax, Lexicography, Additive Weighting, Effectiveness Index, Utility Theory, Tradeoffs, and Nonmetric Scaling. Similarities and differences in the various approaches are demonstrated by a simplified weapon system-selection problem.
TOPSIS is a multiple criteria method to identify solutions from a finite set of alter-natives based upon simultaneous minimization of distance from an ideal point and maximization of distance from a nadir point. TOPSIS can incorporate relative weights of criterion importance. This paper reviews several applications of TOPSIS using different weighting schemes and different distance metrics, and compares results of different sets of weights applied to a previously used set of multiple criteria data. Comparison is also made against SMART and centroid weighting schemes. TOPSIS was not found to be more accurate, but was quite close in accuracy. Using first-order and second-order metrics were found to be quite good, but the infinite order (Tchebycheff norm, L-∞) was found to decline in accuracy.
Outsourcing is an increasingly important issue pursued by corporations seeking improved efficiency. Logistics outsourcing or third-party logistics (3PL) involves the use of external companies to perform some or all of the firm's logistics activities. This paper proposes an intelligent decision support framework for effective 3PL evaluation and selection. The proposed framework integrates case-based reasoning, rule-based reasoning and compromise programming techniques in fuzzy environment. This real-time decision-making approach deals with uncertain and imprecise decision situations. Furthermore, the integration of different methodologies takes the advantage of their strengths and complements each other's weaknesses. Consequently, the framework leads to a more accurate, flexible and efficient retrieval of 3PL service providers (alternatives) that are most similar and most useful to the current decision situation. Finally, a real industrial application is given to demonstrate the potential of the proposed framework.
The most commonly used measures for evaluating the competing mutual funds are “Treynor Ratio”, “Sharpe Ratio” and “Jensen’s Alpha”. One also uses another measure called the “Information Ratio”. However, it is not clear which measure is the most robust. The purpose of our study is to evaluate the performance of mutual funds under the broad framework of multi-attribute decision analysis approach where each criterion can be taken into consideration in making a final ranking of the mutual funds. In this paper we adopt the concepts of “Ideal” and “Anti-Ideal” solutions as suggested by Hwang and Yoon (1981), and study the extended technique for order preference by similarity to the ideal solution (TOPSIS) method using two different “distance” ideas, namely – “Minkowski’s Lλ metric” and “Mahalanobis” distances. The broad framework with the two aforementioned distances is then applied to evaluate the performance of 82 Taiwanese mutual funds for consecutive 34 months. The empirical results show that using TOPSIS methods incorporated Minkowski’s distance measure to evaluate the mutual funds’ performance perform well.
In this paper, a new method is presented for estimating the environmental efficiency of 15 thermo power plants (TPPs) and their evolution over the years. In particular, the plant environmental efficiency, defined as a function of consumptions, costs and emissions (SO2, NOx, ash, and CO2) are considered, taking into account the fuel adopted. The approach is based on a two-step procedure. Firstly, a “Multi Criteria Decision Making” (MCDM) technique is applied to rank the TPPs as a function of the environmental efficiency. In particular the “Technique for Order Preference by Similarity to Ideal Solution” (TOPSIS) is used to order the plants according the six different criteria. Secondary, the TOPSIS ranking analysis is applied with reference to a fuel pollution indicator proposed in the literature, which makes it possible to consider its “environmental quality”. The integration of the pollution indicator with the TOPSIS ranking makes it possible to obtain a graphical output that shows the comparison of the environmental performances between the different plants analysed in an easy and intuitive manner. In addition, concerning the data available for a number of years, it is also possible to study the TPPs environmental efficiency evolution over time.
In this paper, we develop a method for determining weights of decision makers under group decision environment, in which the each individual decision information is expressed by a matrix in interval numbers. We define the positive and negative ideal solutions of group decision, which are expressed by a matrix, respectively. The positive ideal solution is expressed by the average matrix of group decision and the negative ideal solution is maximum separation from positive ideal solution. The separation measures of each individual decision from the ideal solution and the relative closeness to the ideal solution are defined based on Euclidean distance. According to the relative closeness, we determine the weights of decision makers in accordance with the values of the relative closeness. Finally, we give an example for integrated assessment of air quality in Guangzhou during 16th Asian Olympic Games to illustrate in detail the calculation process of the developed approach.
Case-based reasoning (CBR) solves many real-world problems under the assumption that similar observations have similar outputs. As an implementation of this assumption and inspired by the technique for order performance by the similarity to ideal solution (TOPSIS), this paper proposes a new type of multiple criteria CBR method for binary business failure prediction (BFP) with similarities to positive and negative ideal cases (SPNIC). Assuming that the binary prediction of business failure generates two results, i.e., failure and non-failure, we set the principle of this CBR forecasting method which is termed as SPNIC-based CBR as follows: new observations should have the same output as the positive or negative ideal case to which they are more similar. From the perspective of CBR, the SPNIC-based CBR forecasting method consists of R4 processes: retrieving positive and negative ideal cases, reusing solutions of ideal cases to forecast, retain cases, and reconstruct the case base. As a demonstration, we applied this method to forecast business failure in China with three data representations of a formerly collected dataset from normal economic environment and a representation of a recently collected dataset from financial crisis environment. The results indicate that this new CBR forecasting method can produce significantly better short-term discriminate capability than comparative methods, except for support vector machine, in normal economic environment; On the contrary, it cannot produce acceptable performance in financial crisis environment. Further topics about this method are discussed.
High technology industry must continuously improve product quality and multiple correlated product quality characteristics must be assessed simultaneously due to product complexity. While many Taguchi method applications have addressed a state system problem, dynamic multi-response problems have seldom been examined. This study presents a novel optimization procedure for dynamic multiple responses based on Taguchi’s parameter design. The signal to noise (SN) ratio and system sensitivity are used to assess the performance of each response. Principal component analysis is then performed on the SN values and system sensitivity values to obtain a set of uncorrelated components. The optimization direction for each component is also determined based on the corresponding variation mode chart. Finally, the relative closeness to the ideal solution resulting from the technique for order preference by similarity to ideal solution is determined as an overall performance index for multiple responses. A case study obtained from biological reduction of an ethyl acetoacetate process demonstrates the effectiveness of the proposed procedure.
The technological development of buses with new alternative fuels is considered in this paper. Several types of fuels are considered as alternative-fuel modes, i.e., electricity, fuel cell (hydrogen), and methanol. Electric vehicles may be considered the alternative-fuel vehicles with the lowest air pollution. Hybrid electric vehicles provide an alternate mode, at least for the period of improving the technology of electric vehicles. A hybrid electric vehicle is defined as a vehicle with the conventional internal combustion engine and an electric motor as its major sources of power. Experts from different decision-making groups performed the multiple attribute evaluation of alternative vehicles. AHP is applied to determine the relative weights of evaluation criteria. TOPSIS and VIKOR are compared and applied to determine the best compromise alternative fuel mode. The result shows that the hybrid electric bus is the most suitable substitute bus for Taiwan urban areas in the short and median term. But, if the cruising distance of the electric bus extends to an acceptable range, the pure electric bus could be the best alternative.
This paper deals with the cellular manufacturing system (CMS) that is based on group technology (GT) concepts. CMS is defined as identifying the similar parts that are processed on the same machines and then grouping them as a cell. The most proposed models for solving CMS problems are focused on cell formation and intracellular machine layout problem while cell layout is considered in few papers. In this paper we apply the multiple attribute decision making (MADM) concept and propose a two-stage method that leads to determine cell formation, intracellular machine layout and cell layout as three basic steps in the design of CMS. In this method, an initial solution is obtained from technique for order preference by similarity to the ideal solution (TOPSIS) and then this solution is improved. The results of the proposed method are compared with well-known approaches that are introduced in literature. These comparisons show that the proposed method offers good solutions for the CMS problem. The computational results are also reported.Scope and purposeIn the previous array-based clustering methods, arrays are defined by binary numbers that are indicated as the set of machines that process each part. The main problem of these methods is that grouping parts and machines are made regardless of production volume, operational sequences, production cost, inventory and other production system's limitations.In this paper we consider the previous common problems of array-based clustering methods and apply the logical idea of TOPSIS method for solving the cellular manufacturing system problem in which arrays in the part-machine incidence matrix are defined by operational sequences. The TOPSIS is a multiple attribute decision making (MADM) technique in which the alternatives are ranked by their distances between positive and negative ideal solution.
Decision making problem is the process of finding the best option from all of the feasible alternatives. In this paper, from among multicriteria models in making complex decisions and multiple attribute models for the most preferable choice, technique for order preference by similarity to ideal solution (TOPSIS) approach has been dealt with. In real-word situation, because of incomplete or non-obtainable information, the data (attributes) are often not so deterministic, there for they usually are fuzzy/imprecise. Therefore, the aim of this paper is to extend the TOPSIS method to decision-making problems with fuzzy data. In this paper, the rating of each alternative and the weight of each criterion are expressed in triangular fuzzy numbers. The normalized fuzzy numbers is calculated by using the concept of α-cuts. Finally, a numerical experiment is used to illustrate the procedure of the proposed approach at the end of this paper.
The multiple criteria decision making (MCDM) methods VIKOR and TOPSIS are based on an aggregating function representing “closeness to the ideal”, which originated in the compromise programming method. In VIKOR linear normalization and in TOPSIS vector normalization is used to eliminate the units of criterion functions. The VIKOR method of compromise ranking determines a compromise solution, providing a maximum “group utility” for the “majority” and a minimum of an individual regret for the “opponent”. The TOPSIS method determines a solution with the shortest distance to the ideal solution and the greatest distance from the negative-ideal solution, but it does not consider the relative importance of these distances. A comparative analysis of these two methods is illustrated with a numerical example, showing their similarity and some differences.