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Standard and mean deviation methods for linguistic group decision making and their applications
Abstract
This paper proposes two methods for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. Based on the ideal that the attribute with a larger deviation value among alternatives should be assigned a large weight, two methods named standard deviation method and mean deviation method are proposed to determine the optimal weighting vector objectively under the assumption that attribute weights are completely unknown. Two numerical examples are examined using the proposed methods to show the advantages from the other methods. It is shown that the proposed methods are straightforward and no loss of information.
... In this circumstance, we should determine the attribute weights firstly. There are many methods for obtaining attribute weights (Dong, Xiao, Zhang, & Wang, 2016;Jin, Ni, Chen, Li, & Zhou, 2016;Xu & Da, 2010;Yager, 1988;Zhou, Chen, & Liu, 2012), which can mainly be divided into two categories: objective weighting methods Jin et al., 2016;Xu & Da, 2010;Yager, 1988) and subjective weighting methods Zhou et al., 2012). Objective weighting methods are based on some mathematical models where DMs fail in determining the relative importance of attributes, while subjective weighting methods determine the weighting vector based on preferences of DMs. ...
... In this circumstance, we should determine the attribute weights firstly. There are many methods for obtaining attribute weights (Dong, Xiao, Zhang, & Wang, 2016;Jin, Ni, Chen, Li, & Zhou, 2016;Xu & Da, 2010;Yager, 1988;Zhou, Chen, & Liu, 2012), which can mainly be divided into two categories: objective weighting methods Jin et al., 2016;Xu & Da, 2010;Yager, 1988) and subjective weighting methods Zhou et al., 2012). Objective weighting methods are based on some mathematical models where DMs fail in determining the relative importance of attributes, while subjective weighting methods determine the weighting vector based on preferences of DMs. ...
... Due to complexity and uncertainty in many MAGDM problems, with human thinking is inherently subjective, the information about attribute weights maybe unknown, we must determine the attribute weights in advance. Based on the maximizing deviation method (Xu & Da, 2010), here we extend it to the SVN2TL environment. Firstly, we define the deviation degree between any two SVN2TLEs, which is on the basis of Hamming distance measure, is defined as follows: be two SVN2TLEs, then the Hamming distance measure between any two SVN2TLEs is defined as ...
... For example, when evaluating the ''comfort'' of a car, an expert may provide his/her opinion with uncertain linguistic variable like ''between 'fair' and 'good''' [4]. To aggregate linguistic information and uncertain linguistic information, Xu [5][6][7][8] defined some operational laws of linguistic variables and uncertain linguistic variables, and based on which, a variety of linguistic aggregation operators and uncertain linguistic aggregation operators have been developed in the past few decades, such as the linguistic weighted averaging (LWA) operator [9], the extended geometric mean (EGM) operator [10], extended ordered weighted geometric (EOWG) operator [10], extended arithmetical averaging (EAA) operator [10], extended ordered weighted averaging (EOWA) operator [10], linguistic weighted arithmetic averaging (LWAA) operator [11,12], linguistic weighted geometric averaging (LWGA) operator [5], linguistic ordered weighted geometric averaging (LOWGA) operator [5], linguistic hybrid geometric averaging (LHGA) operator [5], linguistic generalized power average (LGPA) operator [13], weighted linguistic generalized power average (WLGPA) operator [13], linguistic generalized power ordered weighted average (LGPOWA) operator [13], linguistic power ordered weighted average (LPOWA) operator [4], linguistic power ordered weighted geometric average (LPOWGA) operator [4], linguistic power ordered weighted harmonic average (LPOWHA) operator [4], linguistic power ordered weighted quadratic average (LPOWQA) operator [4], linguistic power average (LPA) operator [4], linguistic weighted PA operator [4], uncertain linguistic ordered weighted (ULOWA) operator [6], uncertain linguistic weighted averaging (ULWA) operator [6], [14], [15], uncertain linguistic hybrid aggregation (ULHA) operator [6], induced uncertain linguistic OWA (IULOWA) operator [16], uncertain linguistic geometric mean (ULGM) operator [17], uncertain linguistic weighted geometric mean (ULWGM) operator [17], uncertain linguistic ordered weighted geometric (ULOWG) operator [17], induced uncertain linguistic ordered weighted geometric (IULOWG) operator [17], uncertain linguistic PA operator [4], uncertain linguistic weighted PA operator [4], and uncertain linguistic power ordered weighted average (ULPOWA) operator [4], etc. ...
... In Section 5, a numerical example is given to illustrate the developed group decision making method. Section 6 performs a comparison analysis between our new operators and approach and other uncertain linguistic aggregation operators and MAGDM methods [4,6,[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], and then highlights the advantages of the new operators and approach. Finally, Section 7 ends the paper with some concluding remarks. ...
... Especially, if 1 , then (13)-(16) reduce to (5)-(8); if 2 , then (13)-(16) reduce to (9)- (12).. ...
... Peta kemungkinan kemunculan kulit diperoleh berdasarkan euclidean distance (D) (Lagerstrom & Buckley, 2012) atau jarak kesamaan vector kulit dan non-kulit dihitung dalam ruang kemunculan kulit pada setiap piksel x dari referensi piksel r, euclidean distance dapat didefinisikan sebagai: Wang & Luo, 2010). Standar deviasi dan rata-rata deviasi banyak diusulkan untuk menentukan bobot vektor yang optimal secara objektif dengan asumsi bobot atribut sudah diketahui (Xu & Da, 2010). Oleh karena itu, pada penelitian ini untuk mengukur tingkat kesalahan deteksi kulit salah satunya menggunakan standar deviasi untuk mengetahui keragaman suatu kelompok data kulit dan non-kulit. ...
... Hasil ekperimen terdapat 555 data dari database IBTD, merupakan nilai jarak piksel kulit dan non-kulit dari proyeksi kelas pertama dan kelas kedua hasil komparasi antara SPM dan DT. Nilai standar deviasi untuk menentukan bobot vektor yang optimal secara objektif dengan asumsi bobot atribut sudah diketahui (Xu & Da, 2010), seperti yang ditunjukan pada Tabel 3. Dari perhitungan seluruh dataset yang digunakan, nilai 94% merupakan bagian dari piksel kulit yang benar diklasifikasikan sebagai kulit dihitung dengan (Recall) ηtp= TP/(FN+TP). Nilai 6,13% merupakan bagian pengelompokan piksel kulit sebagai background dihitung dengan δfn= FN/(FN+TP) dan nilai 34% merupakan bagian pengelompokan piksel background sebagai kulit dihitung dengan δfp= FP/ (FP+TN). ...
Deteksi kulit memainkan peranan penting dalam berbagai aplikasi pengolah citra, mulai dari deteksi wajah, pelacakan wajah, penyaringan konten pornografi, berdasarkan sistem pencarian citra dan berbagai domain interaksi manusia dan komputer. Pendekatan informasi warna dapat mendeteksi warna kulit dengan baik menggunakan skin probability map (SPM) dengan aturan bayes. Namun SPM memiliki permasalahan dalam mendeteksi tekstur kulit. Linear discriminant analysis (LDA) merupakan algoritma ekstraksi fitur, dalam deteksi kulit digunakan untuk mengekstrak fitur tekstur kulit yang dapat menangani masalah SPM. Namun LDA memiliki permasalahan apabila digunakan untuk mengekstrak fitur tekstur kulit pada kernel yang berbeda. Distance transform (DT) merupakan algoritma untuk menghitung jarak citra biner pada setiap pikel gambar dan fitur poin terdekatnya, DT merupakan algoritma yang dapat mengatasi masalah pada LDA. Kombinasi algoritma SPM, LDA dan DT diusulkan untuk memperbaiki performa dari kemunculan kulit pada deteksi kulit. Dataset pada metode yang diusulkan menggunakan IBTD dataset. Hasil dari metode yang diusulkan bahwa metode yang diusulkan menunjukan peningkatan akurasi deteksi kesalahan yang signifikan pada SPM dan LDA.
... According to the applied data systems, there could be two parts with respect to the objective methods, one is named ISOM (objective method for information system) and the other one is called DSOM (objective method for decision system). However, to the best of our knowledge, most of objective weight assignment methods are aimed at IS, such as Entropy method [4,23,24], Principal Components Analysis (PCA) method [25], criteria importance through inter-criteria correlation (CRITIC) method [16], modifying TOPSIS method [14], standard deviation (SD) and mean deviation (MD) method [26], correlation coefficient and standard deviation (CCSD) method [15] and some other weight assignment methods in different issues (see, e.g., [27][28][29] and the references therein). Nevertheless, there are few relevant studies on DS. ...
... In this subsection, we select some commonly used objective weight determination methods and some mature and latest methods that can produce the weights of DS as comparisons to illustrate the advantage of the proposed method. Therein, the objective methods are Entropy method [4], CRITIC [16], SD [26] and CCSD [15], and the other ones are GRA [30], CE [31], NRS [32], FDAF [34] and DR-JMIM [35]. In the GRA model, we take the decision attribute as the optimal one to measure the importance degrees of conditional attributes, which could be considered as the weights of attributes. ...
Attribute weight assignment plays a key role in multiple attribute decision making (MADM). For the issue of labeled multiple attribute decision making (LMADM), the existing methods of attribute weight determination that have been well developed for MADM usually ignore or do not take full advantage of the supervisory function of labels. As a result, the weights produced by these methods may not be ideal in practice. To make up for this deficiency, this paper develops an objective method based on Bayes risk. Specifically, the LMADM problem is first put forward, then a Gaussian kernel based loss function is proposed to cope with the drawback that the loss function in Bayes risk is usually determined by experts. Meanwhile, Mahalanobis distance and fuzzy neighborhood relationship are employed to measure the fuzziness of data set. Finally, a number of experiments, including the comparison experiments on UCI data and the effectiveness evaluation of fighter, are carried out to illustrate the superiority and applicability of the proposed method.
... where a k j ¼ 1 n P n it¼1 a k tj represents the average value of an expert for m indicators. The term dða k ij ; a k j Þ ¼ a k ij À a k j (Xu, 2007;Xu and Da, 2011) represents the deviation of mean value a k j from the indicator values a k ij of the alternative x i for the expert e k and the indicator c j . Thus, S k j denotes the standard deviation for the expert e k of the indicator c j . ...
... A Lagrange function can be formed using the results from the literature review (Xu and Da, 2011): ...
Green construction is to conserve the resources and reduce the negative impact of construction activities on the environment to the maximum extent, with scientific management and technological progress under the premise of ensuring the quality, safety and other basic requirements. Recent years, accompanied by the rapid development of construction industry, a considerable proportion of energy and resources, particularly high-carbon materials, is consumed in the construction activities, emitting mass greenhouse gases, which have a damaging impact on the environment. This is especially for the mega public projects. Therefore, under the green and sustainable perspective, actions to control carbon dioxide (CO2) emissions in the construction industry are imperative. In this case, if CO2 emissions reduction can be considered beforehand during the bid evaluation stage, contractors will be guided by bid evaluation indicators and therefore improve their construction schemes, enabling the construction phase to be green, energy saving and sustainable. This is because bid evaluation indicators can serve as guiding effect on the contractors. Given that CO2 emissions are rarely given sufficient consideration in traditional bid evaluation, this study conducts a systematic analysis to identify major sources of CO2 in construction phase and attempts to develop a conceptual computational model in terms of CO2 emission. Then, a linguistic group decision-making framework for bid evaluation in mega public projects considering CO2 emissions reduction is developed. In this framework, entropy, relative entropy, the standard deviation method and weighted aggregation operators are applied to determine the indicator weights, the expert weights and the information aggregation in bid evaluation decision-making. Finally, a scenario comparison between the proposed linguistic group decision-making bid evaluation framework and the traditional framework is made through a case study, and the scientific basis and reliability of this new framework are validated. The establishment of this framework can enrich the decision-making methods in construction management field. And it can provide meaningful reference for owners to choose the most qualified contractors and spur contractors to improve their construction schemes, enabling construction phase to be green, energy saving and sustainable.
... In this case, multiple decision-makers are required to participate in the decision process and the multiattribute group decision-making (MAGDM) appears. Nowadays, MAGDM has attracted many researchers' attention and has become a hot research topic [1][2][3][4][5][6][7][8][9]. ...
... (1) our proposed method considers the information of the decision object in different periods, so it can comprehensively describe the decision object and obtains more reasonable results; (2) in the process of constructing period significance coefficients optimization model, the information influence degree in different periods on the decision results and the volatility of the decision environment are considered, which will help to obtain more stable period significance coefficients; (3) triangular fuzzy numbers are used to represent the decision information, which not only can express the interval ranges of the decision information but also can highlight the gravity center having the largest probability. In addition, triangular fuzzy numbers can make up the deficiencies of the interval number in precision and facilitate the decisionmaking at least to some extent. ...
This paper proposed a new multiattribute group decision-making method, in which the period significance coefficients and the attribute significance coefficients are completely unknown, and the attribute values are triangular fuzzy numbers. At first, to obtain the period significance coefficients, the period significance coefficients optimization model is constructed according to the time degree and the differences of the decision information in different periods. Then, attribute significance coefficients are determined by the maximum deviation method. Based on this, alternatives are ranked by the triangular fuzzy ratio system method, the triangular fuzzy reference point method, and the triangular fuzzy full multiplicative form, respectively. The dominance theory is used for aggregating the subordinate rankings into the final ranking. Finally, a numerical example is presented to illustrate the feasibility and effectiveness of the proposed method.
... In the past few decades, many scholars have developed a variety of linguistic aggregation operators, which can be classified into the following categories [10]: (1) The linguistic aggregation operators, which are based on linear ordering [11][12][13][14][15][16]; (2) The linguistic aggregation operators, which are based on the extension principle [17][18][19][20] and make computations on the fuzzy numbers that support the semantics of the linguistic labels [21][22][23][24][25]; (3) The linguistic aggregation operators, which are based on symbols [8,26,27], and make computations on the indexes of the linguistic labels; (4) The linguistic aggregation operators, which are based on a 2-tuple fuzzy linguistic representation model [28][29][30][31][32][33][34][35][36]. This model represents the linguistic assessment information by means of a pair of values called 2-tuples, composed by a linguistic term and a number; and (5) The linguistic aggregation operators, which compute directly with words [10,[37][38][39][40][41][42][43][44][45][46][47][48][49][50]. The operators in (1)-(3) develop approximation processes to express the results in the initial expression domain, that produce a consequent loss of information and hence a lack of precision. ...
... be a finite and completely ordered discrete linguistic term set with odd cardinality, where i s represents a possible value for a linguistic variable and 1 g + is the number of granularity in the linguistic term set. As an illustration, a set of seven terms S could be given as follows [40,45,48,49,63,64,65]: ...
... The evaluation of bank loan project involves many assessment indexes, some of which are difficult to describe by using quantitative data. In this case, decision makers are more inclined to use linguistic variables to give evaluation information [1][2][3]. The cloud model is a model that takes a natural language value as a starting point to achieve the uncertainty conversion between qualitative concept and quantitative numerical values, which can well overcome the shortage of probability theory and fuzzy mathematics in dealing with uncertainty. ...
... C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 Step4: Determine the positive ideal solution and negative ideal one by Eqs. (3) and (4), as shown in Table 7. x x x f f , so 3 x is the best alternative. ...
... The deviation method is a commonly used objective weighting method. The deviation method indicates that the greater the change in the index value of an indicator, the more information the indicator carries, and a greater weight should be given [31,32]. However, the deviation method cannot be applied to calculate weights for interval values and requires improvement based on the interval theory. ...
The seasonality of floods is a key factor affecting riparian agriculture. Flood season staging is the main means of identifying the seasonality of floods. In the process of staging the flood season, set pair analysis is a widely used method. However, the set pair analysis method (SPAM) cannot take into account the differences in and volatility of the staging indicators, and at the same time, the SPAM cannot provide corresponding staging schemes according to different scenarios. To address these problems, the improved set pair analysis method (ISPAM) is proposed. Kernel density estimation (KDE) is used to calculate the interval of the staging indicators to express their volatility. Based on the interval theory, the deviation method is improved, and the weights of the staging indicators are calculated to reflect the differences in different staging indicators. The theoretical correlation coefficient can be calculated by combining the weights and interval indicators and fitting the empirical connection coefficient corresponding to each time period. Finally, the ISPAM is established under different confidence levels to derive staging schemes under different scenarios. Based on the daily average precipitation flow data from 1961 to 2022 in the Nandujiang middle basin and surrounding areas in tropical island regions, the staging effect of the ISPAM was verified and compared using the SPAM, Fisher optimal segmentation method, and improved set pair analysis method without considering differences in the indicator weights (ISPAM-WCDIIW), and the improved set pair analysis method without considering indicator fluctuations (ISPAM-WCIF). According to the evaluation results from the silhouette coefficient method, it can be concluded that compared with the SPAM and ISPAM-WCIF, the ISPAM provided the optimal staging scheme for 100% of the years in the test set (2011–2022). Compared with the Fisher optimal segmentation method, the optimal staging scheme for more than 83% of the years (2011, 2013–2015, and 2017–2022) in the test set was provided by the ISPAM. Although the ISPAM-WCDIIW, like the ISPAM, can provide optimal staging schemes, the ISPAM-WCDIIW could not provide an exact staging scheme for more than 55% of the scenarios (the ISPAM-WCDIIW could not provide an exact staging scheme in scenarios (0.7, 0.6), (0.8, 0.6), (0.8, 0.9), (0.95, 0.6), and (0.95, 0.8)). The results show that the ISPAM model is more reasonable and credible compared with the SPAM, Fisher optimal segmentation method, ISPAM-WCDIIW, and ISPAM-WCIF. The purpose of this study is to provide a reference for flood season staging research during flood seasons.
... For the weight w i required in linear combination calculation, the commonly used calculation methods include equal weight method, variance reciprocal method, residual reciprocal method, and standard deviation method (Xu and Da 2010;Qu and Bai 2018). In order to explore a more accurate and effective prediction model, this paper will compare and analyze these four methods for calculating weights mentioned above, so as to determine the best performing temperature prediction model. ...
In recent years, under the influence of changes in natural conditions and human social activities, the issue of global warming has become increasingly prominent. So it is crucial to effectively predict the future trend of temperature changes. In this regard, from the perspective of statistical models, this paper studies a new combination model, namely the new GM-ARIMA model, based on linear combination of weight calculation. Furthermore, it also analyzes the prediction effect through comparative experiments and uses multiple performance evaluation indicators, so as to prove the scientificity and effectiveness of the proposed combination model in this paper. Finally, according to the experimental results, it can be clearly found that among the four methods for calculating the weights of linear combination, namely the equal weight method, the variance reciprocal method, the residual reciprocal method and the standard deviation method, the combination model using the standard deviation method for calculation has the highest prediction accuracy, so it is finally decided to use this method to build the combination model (namely S-GM-ARIMA). In addition, the experimental results show that the S-GM-ARIMA model achieves the best prediction results compared to other existing prediction models. Among them, the MAE of S-GM-ARIMA decreases by 10.38% and 16.22% compared to the GM(1,1) model and ARIMA model, respectively. The RMSE of S-GM-ARIMA decreases by 4.52% and 10.03% compared to the GM(1,1) model and ARIMA model, respectively. And the MAPE of S-GM-ARIMA decreases by 10.34% and 16.17% compared to the GM(1,1) model and ARIMA model, respectively. Therefore, the new GM-ARIMA combination model studied in this paper has relatively higher prediction accuracy when making predictions, and can be used to make more effective and accurate predictions of global average temperature. This study can also provide reference for countries in making decisions to address global warming issues.
... Determining the indicator weight is crucial for multi-attribute decision making. Under the condition that the indicator weight information is completely unknown and the evaluation value is in the form of a linguistic variable, the deviation method [41] is used here to determine the indicator weight. This method is suitable for situations where the evaluation value is in the form of a linguistic variable. ...
Hydrogen leakage and explosion accidents have obvious dangers, ambiguity of accident information, and urgency of decision-making time. These characteristics bring challenges to the optimization of emergency alternatives for such accidents. Effective emergency decision making is crucial to mitigating the consequences of accidents and minimizing losses and can provide a vital reference for emergency management in the field of hydrogen energy. An improved VIKOR emergency alternatives optimization method is proposed based on the combination of hesitant triangular fuzzy set (HTFS) and the cumulative prospect theory (CPT), termed the HTFS-CPT-VIKOR method. This method adopts the hesitant triangular fuzzy number to represent the decision information on the alternatives under the influence of multi-attributes, constructs alternatives evaluation indicators, and solves the indicator weights by using the deviation method. Based on CPT, positive and negative ideal points were used as reference points to construct the prospect matrix, which then utilized the VIKOR method to optimize the emergency alternatives for hydrogen leakage and explosion accidents. Taking an accident at a hydrogen refueling station as an example, the effectiveness and rationality of the HTFS-CPT-VIKOR method were verified by comparing with the existing three methods and conducting parameter sensitivity analysis. Research results show that the HTFS-CPT-VIKOR method effectively captures the limited psychological behavior characteristics of decision makers and enhances their ability to identify, filter, and judge ambiguous information, making the decision-making alternatives more in line with the actual environment, which provided strong support for the optimization of emergency alternatives for hydrogen leakage and explosion accidents.
... The technique that determines the weights of objectives according to their standard deviations is called the Standard Deviation weighting technique. It is used as an alternative objective weighting technique in MCDA studies (Xu & Da, 2010). The steps of the technique are summarized below. ...
Organizational performance is crucial in determining the position of a company within its industry. Especially with financial performance, the positive and negative aspects of the company can be determined with comparisons to similar companies, in an effective and practical fashion. In this study, in which companies operating in the mining sector that contribute to the development of many industries are examined, financial performance analysis is made and all companies operating in the relevant sector in Borsa Istanbul are ranked according to their performance. In this study, 7 quarterly periods between 2021 and 2022 were examined, 6 accounting and valuation-based criteria were used and standard deviation weighting technique was preferred. Interestingly, although the two methods generated different successful performers, they produced similar results, in terms of financial performance. Thus, GRA and TOPSIS methods are suggested to financial decision makers as a decision support system in their strategical decisions.
... Wang and Luo (2010) combined the SD-based model with correlation coefficient for determining the weights of attributes in MADA problems. Xu and Da (2010) introduced two models using the SD and mean deviation tool to solve the MADA problems with linguistic information. Peng and Yuan (2021) extended the SD method under Pythagorean fuzzy environment and combined with a MADA method for solving decision-making problems. ...
Purpose
This paper develops a decision-analysis model to prioritize and select the site to establish a new hospital over different indicators such as cost, market conditions, environmental factors, government factors, locations and demographics. In this way, an integrated model is proposed under the intuitionistic fuzzy information (IFI), the standard deviation (SD), the rank-sum (RS) and the measurement of alternatives and ranking using the compromise solution (MARCOS) approach for ranking hospital sites (HSs).
Design/methodology/approach
The IF-SD-RS model is presented to obtain the combined weight with the objective and subjective weights of diverse sub-criteria and indicators for ranking sites to establish the hospital. The IF-MARCOS model is discussed to prioritize the various sites to establish the hospital over several crucial indicators and sub-criteria.
Findings
The authors implement the developed model on a case study of HSs assessment for the construction of new hospital. In this regard, inclusive set of 6 key indicators and 18 sub-criteria are considered for the evaluation of HSs. This study distinguished that HS ( h 2 ) with combined utility function 0.737 achieves highest rank compared to the other three sites for the given information. Sensitivity analysis is discussed with different parameter values of sub-criteria to examine how changes in weight parameter ratings of the sub-criteria affect the prioritization of the options. Finally, comparative discussion is made with the diverse extant models to show the reasonability of the developed method.
Originality/value
This study aims to develop an original hybrid weighting tool called the IF-SD-RS model with the integration of IF-SD and IF-RS approaches to find the indicators' weights for prioritizing HSs. The developed integrated weighting model provides objective weight by IF-SD and subjective weight with the IF-RS model. The model presented in the paper deals with a consistent multi-attribute decision analysis (MADA) concerning the relations between indicators and sub-criteria for choosing the appropriate options using the developed IF-SD-RS-MARCOS model.
... The deviation maximization approach is exploited to evaluate the weight according to the dispersion of the attribute value for the indicator [31]. This method can realize the dynamic adjustment with the variation of index data, and thereby, it can be more appropriately applied to the optimization of the desert railway alignment scheme. ...
The construction of desert railways inevitably destructs the environment and aggravates the wind–sand damage along the line. A reasonable railway route is an effective measure to avoid blown sand hazards, save construction costs, and reduce environmental damage. Currently, the selection methods for the railway route scheme are to analyze the qualitative indicators and quantitative indicators separately, and there are few decision-making models for the desert railway scheme. Therefore, this study aims to propose a comprehensive quantitative optimization model of the route scheme for the desert railway. Based on the design principles of hazard reduction, the evaluation index system of the desert railway route is first constructed, including railway design factors, wind-blown sand hazard factors, environmental impact factors, and operation condition factors. Subsequently, the subjective weights and objective weights are combined to obtain the comprehensive weights of the index by utilizing the principle of minimum discrimination information. Finally, the interval number is employed to quantify the linguistic fuzzy number of qualitative indicators, and the optimization model of the route scheme for the desert railway is constructed based on the technique for order preference by similarity to an ideal solution (TOPSIS). The model is verified using the Minfeng-Yuhu section in the Hotan–Ruoqiang railway as the case study. The achieved results reveal that this model enhances the accuracy and efficiency of the railway scheme decision-making and provides a theoretical basis for the optimal design and sand damage control of the desert railway.
... As is known, the usual resolution scheme for linguistic MAGDM is composed of the aggregation phase and the exploitation phase. In first phase, individual decision matrices are aggregated to an overall one by reasonable linguistic aggregation operators, such as those in [4,7,11,18,19,[25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Among these linguistic aggregation operators, the power ones, developed by the classical power average and geometric operators [39,40] and featuring their discounted weighting on the outer input arguments, are of great importance from the perspective of the consensus degree in aggregation. ...
To evaluate fuzzy information precisely, researchers and practitioners are apt to use linguistic variables to model vague or uncertain contexts in natural language. In this paper, some new operation laws for continuous linguistic terms using strict t-norms and t-conorms are defined. Significantly, these operation laws have some desirable properties and are closed on the restricted continuous linguistic term set. On the basis of these new linguistic operation laws, a series of triangular t-(co)norm-based linguistic generalized power geometric operators are developed. In order to consider the interactive influence and interrelationship of decision makers (DMs) and attributes, a decision-making trial and evaluation laboratory (DEMATEL)-based method for linguistic multiple attributes group decision making (MAGDM) is proposed. In the method, the weighting information for DMs and attributes are dependent on the initial direct-relation matrices among DMs and attributes, respectively. Finally, a numerical example is provided. In comparison with the existing methods, two aspects of the DEMATEL-based method for linguistic MAGDM in the work can be highlighted: the underlying operators for linguistic terms using strict t-norms and t-conorms that are closed on the set of the restricted continuous linguistic term set; and the techniques in determining the weighting information, with which the weighting information for DMs and attributes are determined by the interactive influence and interrelationship among DMs or attributes.
... Finally, weights are determined for each period depending on the calculated SDs [38] (see Table 3). This weighting method is mostly applied to solve complex and unclear problems in MCDM studies [46]. Table 3. Stages of Standard Deviation (SD) Model [38]. ...
A major difficulty in comparing and even choosing MCDM methods is the uncertainty of information about the consistent and unique characteristics of the results produced. The objective information content of the final scores produced by MCDM methods and their relevance to real life can give us an important idea about them. In this study, first of all, seven MCDM methods with different methodologies were applied to evaluate companies’ financial performance. Then, the obtained MCDM scores were compared using two different objective verification mechanisms. The first validation criterion is the relationship of a MCDM method to real-life rankings (share price). The second criterion is the standard deviation (SD) technique used to discover the objective information content of MCDM final scores. According to the results of this study, PROMETHEE and FUCA definitely outperform other methods in terms of both SD values and strength of correlation with reference real-life rankings. Also, FUCA is methodologically simpler than other methods. However, it produced nearly identical results as the sophisticated PROMETHEE method.
... Compared with other objective weighting methods, it fully extracts all the information contained in the indexes, which is more conductive to obtain credible evaluation results (Yalcin and Ünlü 2018). The degree of data variation can be measured using standard deviation or mean deviation (Xu and Da 2010). The traditional CRITIC method uses standard deviation to reflect the degree of data variation. ...
This study uses hierarchical cluster analysis (HCA) to screen the evaluation indexes and establishes a comprehensive evaluation index system for water resources carrying capacity (WRCC), based on the VIKOR method and the obstacle degree model for the identification of the main factors affecting the WRCC of Weifang City. The results show that the WRCC of Weifang City has steadily increased from 2008 to 2018. The subsystems referred to society and water environment are currently the main obstacles affecting Weifang’s WRCC, but there is still space for improvement in the future. The areas with low WRCC was Kuiwen District in 2018, which was in a seriously overloaded state, mostly affected by the water resources subsystem. The implementation of measures such as efficiently improving the level of water resources management and the development of water conservancy projects is prominent in water resource planning in Kuiwen District. This study analyzes the current situation of water resources management in order to consider it in strategic decision-making in promoting the improvement of WRCC, which in turn may ensure the realization of a green and sustainable development strategy in the future for Weifang City.
... To expert e k and indicator A j , the standard deviation between region R i and others is as follows [45]: ...
The operation of emergency logistics plays a prominent role in reducing the consequences of disasters. Based on the establishment of a comprehensive evaluation system with the whole period of the disaster cycle that covers emergency preparation, response, and recovery, this paper proposes a fuzzy-symmetrical Technique for Order Preference by Similarity to Ideal Solution-Entropy Weight (TOPSIS-EW) method with multi-granularity linguistic assessment (MGLA) information to evaluate the performance of emergency logistics. Furthermore, the proposed evaluation method is employed to evaluate the performance of emergency logistics in Wenchuan earthquake, five worst-hit regions (i.e., Wenchuan County, Beichuan County, Qingchuan County, Mianzhu City, Shifang City) were ranked as V, III, I, II, IV, respectively. Finally, the effectiveness and reliability of the method are verified by comparison with the other two related methods and a sensitivity analysis. Based on the comprehensive evaluation results, some specific managerial suggestions are proposed to improve the emergency logistics capacity.
... Thereby, the weighted standard decision matrix can be calculated as follows [38,39]: ...
The paper focuses on the problem of traffic congestion at intersection based on the mechanism of risk identification. The main goal of this study is to explore a new methodology for identifying and predicting the intersection congestion. Considering all the factors influencing the traffic status of intersection congestion, an integrated evaluation index system is constructed. Then, a detailed dynamic decision model is proposed for identifying the risk degree of the traffic congestion and predicting its influence on future traffic flow, which combines the traffic flow intrinsic properties with the basic model of the Risking Dynamic Multi-Attribute Decision-Making theory. A case study based on a real-world road network in Baoji, China, is implemented to test the efficiency and applicability of the proposed modeling. The evaluation result is in accord with the actual condition and shows that the approach proposed can determine the likelihood and risk degree of the traffic congestion occurring in the intersection, which can be used as a tool to help transport managers make some traffic control measures in advance.
... So, the study of determining attribute weight by maximizing deviation draws the attention of scholars [69,70]. In addition, Xu and Da [71] and Xu [72] put forward some similar methods, namely maximizing standard deviation method and maximizing mean deviation method, to determine attribute weights for different data forms. Based on the idea of maximizing deviations in literature [69], this paper determines the attribute weights in the heterogeneous information environment. ...
Aiming at the decision-making problem in heterogeneous information environment and considering the influence of decision makers' psychological behavior on decision-making results, this paper proposes a multi-attribute decision-making method based on prospect theory in heterogeneous information environment. The heterogeneous information in this paper indicates that the decision attribute value is represented by various types of data forms, including exact number, interval number, linguistic term, intuitionistic fuzzy number, interval intuitionistic fuzzy number, neutrosophic numbers, and trapezoidal fuzzy neutrosophic numbers, and so on. Firstly, the distance and similarity measure of various heterogeneous data are introduced, and the heterogeneous information attribute weights are obtained using the deviation maximization method. Then, the psychological expectation value of each attribute given by the decision maker is used as a reference point, thereby calculating the gain and loss of each attribute value relative to the reference point, and establishing a gain matrix and a loss matrix. On this basis, the prospect theory is used to obtain the comprehensive prospect value of each alternative, so as to obtain the alternative ordering result and optimal alternative. Finally, an illustrative example about typhoon disaster assessment is presented to show the feasibility and effectiveness of the proposed method, and the advantages of the proposed method are illustrated by comparison with other methods.
... In addition, some researchers focused on computing the objective attribute weights based on the dispersion of ranging data in the decision matrix, such as the entropy method (Garg, 2015), the multi-objective programming approach (Kannan, Khodaverdi, Olfat, Jafarian, & Diabat, 2013), and the deviation method (Xu & Da, 2010). The limitation of these types of weight-determining methods is the poor generalization ability. ...
Innovative ability plays a critical role in the sustainable development of universities. Although the assessment of universities' innovative ability is a significant undertaking, it is difficult work. This challenge can be addressed as a typical multiple attribute decision making (MADM) problem, in which multiple attributes should be considered with different levels of importance. This paper aims to propose an integrated MADM method to solve this issue. To do so, we first introduce the least square method with the hesitant fuzzy linguistic term set to determine the subjective attribute weights. Considering that the selected attributes are not always in conflict with each other due to the complexity of objective things, we further present a correlation coefficient‐based method to calculate another kind of attribute weight. The final weights are the combined form of these two types of attribute weights. In addition, we enhance the robust ranking method, MULTIMOORA, with the Borda rule to calculate the utility values of universities and derive their rankings. Finally, after establishing an index system, the assessment of the innovative ability of 26 world‐class construction universities in China is conducted by using the proposed method. The advantages and disadvantages of the assessed universities are analysed.
... Xu and Da extended this method to generate the attribute weight in a uncertain MADM with interval decision information [49]. Furthermore, Xu and Da extended this method to calculate the attribute weight in a linguistic decision information environment [47]. Chang and Cheng created a combination of fuzzy OWA and the DEMATEL method to rank the risk of failure [6]. ...
Owing to the complexity of decision environment, not all the attributes in multiple attribute decision making are quantitative. There are also some qualitative attributes, which are related to the integration of multiple attribute decision making (MADM) and linguistic multiple attribute decision making (LMADM). The specific method for composite multiple attribute decision making (CMADM) problems is crucial for decision maker (DM) to make scientific decision. In this paper, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is extended to a Composite Technique for Order Preference by Similarity to an Ideal Solution (CTOPSIS) method to solve the CMADM problems. As the basis of the CTOPSIS method, the distance measure model in linguistic space and in n-dimension linguistic space is generated based on the non-linear mapping. Based on the distance measure in linguistic space, a standard deviation method is taken to get the attribute weight. At the same time, the distance measure models are proposed based on the distance measure in n-dimension linguistic space, which are used to calculate the distance between the alternatives and the positive and negative idea points separately. Furthermore, a CTOPSIS method is generated to solve the CMADM problems. Finally, a numerical example is illustrated to explain the process. And the result shows that the CTOPSIS method is quite practical and more approximate to the real decision making situation.
... A number of literatures have recently investigated group decision making under linguistic environment [18][19][20][21][22][23][24][25]. Xu & Da [26] proposed two methods named standard deviation method and mean deviation method to determine the optimal weighting vector. The method is based on the idea that the attribute with a smaller deviation value among alternatives should be assigned a small weight. ...
An effective method is proposed to solve the group decision making problems with uncertain multiplicative linguistic information. Firstly, to compare two uncertain multiplicative linguistic variables, a possibility degree formula is introduced in accordance with the operation laws. Some desirable properties of possibility degree are provided. Then, the uncertain multiplicative linguistic hybrid weighted geometric averaging (ULHWG) operator is developed to aggregate uncertain multiplicative linguistic variables into an overall preference value. Thus, a comprehensive algorithm for linguistic group decision making is proposed based on the deviation measure and ULHWG operator. Finally, a numerical example is provided to illustrate the practicality and validity of the proposed method.
... The proposed method based on the mean and standard deviation of scores called EFQM is summarized in the following steps: -Step 1: The mean score of each of indicators of performance is computed based on the results of questionnaire. We assume the mean score of index i is equal -Step 2: Based on the standard deviation and ranging of performance indicators by different respondents, we can compute the weight of importance called the weight of importance based on standard deviation as follows proposed in the study of Xu and Da (2010). In this method, we assume that k = 1,…,i is the index of respondents and the score in questionnaire stating the k th respondent for i th index is ...
Performance assessment is used to identify the best companies and to present the effective solutions for the purpose of improving performance of cooperative companies. Thus, improving the assessment tools enhance the performance rank of the cooperative companies. In this study, a fuzzy model based on Sogno-Mamdani inference system was proposed to evaluate the performance of cooperative companies. In the proposed fuzzy rule based model, the knowledge base was created using a questionnaire tool to collect the experts’ knowledge in terms of the coefficient of performance assessment indicators in the cooperative companies. Then, the proposed weighting method was used to find the rules in the fuzzy inference system. Moreover, an Indicator Ranking Method based on the EFQM method was used to find the best indicators effectively improve the company performance. The results of study showed that in the proposed performance assessment model, trade indicators and social responsibility are much important compared to the conventional models in the performance assessment of cooperative companies. Moreover, education is the most effective indicator to enhance the performance of cooperative companies.
... Until now, many linguistic aggregation operators have been proposed and these operators can be classified into six types: (1) the first is based on linear ordering, such as the linguistic max and min operators [10][11][12], linguistic max-min weighted averaging operator [13], linguistic median operator [14], ordinal ordered weighted averaging operator [15], linguistic weighted conjunction operator [16]; (2) The second is built on the extension principle [17,18] and makes computations on fuzzy numbers that support the semantics of the linguistic labels, such as the linguistic OWA operator [19], and the linguistic weighted OWA operator [20], the inverse linguistic OWA operator degree [21], distance measure operator with linguistic information [22], induced linguistic continuous ordered weighted geometric operator [23], linguistic distances with continuous aggregation operator [24], linguistic probabilistic weighted average operator [25]; (3) The third is based upon 2-tuple representation, including the 2-tuple arithmetic mean operator [26], 2-tuple OWA operator [27], dependent 2-tuple ordered weighted geometric operator [28], 2-Tuple linguistic hybrid arithmetic aggregation operator [29]; (4) The fourth computes directly with words, such as the linguistic weighted averaging operator [30], extended ordered weighted geometric operator [31], linguistic weighted arithmetic averaging operator [32], linguistic ordered weighted geometric averaging operator [33], uncertain linguistic weighted averaging operator [34], induced uncertain linguistic OWA operator [35], uncertain linguistic geometric mean operator [36]; (5) The fifth is on the basis of the power ordered weighted average operator [37], including linguistic power ordered weighted average (LPOWA) operator [38], the linguistic generalized power average (LGPA) operator [39]; (6) and the last is a class of cloud aggregation operator which introduces the cloud model [40], in LMCGDM, such as the cloud weighted arithmetic averaging (CWAA) operator and cloud weight geometric averaging (CWGA) operator [41], trapezium cloud ordered weighted arithmetic averaging (TCOWA) operator [42]. A detail description of the operators LPOWA, CCWA, and CWGA will be presented in Section 2 of the paper. ...
In this paper, we develop a new linguistic aggregation operator based on the cloud model for solving linguistic group decision-making problem. First, an improved generating cloud method is proposed so as to transform linguistic variables into clouds, which modifies the limitation of the classical generating cloud method. We then address some new cloud algorithms, such as cloud possibility degree and cloud support degree which can be respectively used to compare clouds and determine the weights. Combining the cloud support degree with power aggregation operator, we develop a new cloud aggregation operator dubbed the cloud generalized power ordered weighted average (CGPOWA) operator. We study the properties of the CGPOWA operator and investigate its family including a wide range of aggregation operators such as the CGPA operator, CPOWA operator, CPOWGA operator, CPWQA operator, CWAA and CWGA operator. Furthermore, a new approach for linguistic group decision-making is presented on the basis of the improved generating cloud method and CGPOWA operator. Finally, an illustrative example is provided to examine the effectiveness and validity of the proposed approach.
... The electronic analytical balance had a measurement accuracy of 0.1 mg and a linear error of ±0.2 mg. The weights as recorded by the electronic analytical balance were used for the calculation of the standard deviation, which was carried out as follows (Thompson 1935;Xu and Da, 2010): ...
Novel hygroscopic carboxymethyl cellulose (CMC) graft copolymer adsorbents (CMC-g-AA and CMC-g-AM) were synthesized by solution polymerization, using CMC as a raw material and acrylic acid (AA)or acrylamide (AM) as a modifying monomer. The influence of synthetic conditions, including the mass ratio of monomer and CMC, degree of neutralization, polymerization temperature, and time on the adsorption performance of the CMC graft copolymer adsorbents were discussed. Based on the optimized conditions, the CMC graft copolymer/silica gel composite adsorbents (CMC-g-AA/B, or CMC-g-AM/B) were obtained by impregnating silica gel type B (B) into copolymer solutions. The compositions, structures, and pore size distributions of the composite adsorbents were characterized using Fourier transform infrared spectroscopy (FTIR) and porosity analysis, while their adsorption/desorption performances, and thermal stabilities were also tested by static and dynamic adsorption, thermogravimetry (TG), and temperature programmed desorption (TPD). Cycle stability was also taken into consideration. The results showed that, the copolymer/silica gel composite adsorbents had excellent adsorption performances compared to silica gel, while their desorption activation energies were slightly increased. This was attributed to the enhanced interaction between the CMC graft copolymers and water molecules. TG analysis and the adsorption/desorption cycles suggested that the composite adsorbents had excellent thermal and cycle stabilities for water vapor adsorption.
... Step 3 also play critical roles in computing the final scores of the scientists (see, for example, [15][16][17]). Thus, if the weights of the criteria can be optimized by other new models, the above extended TOPSIS can be further improved in ranking the IRO of the scientists. ...
Evaluation on achievement of scientists plays an important role in efficiently mining information of human resources. A metrics model, which is employed to calculate the number of academic papers, research awards and scientific research projects, often significantly affects the degree of fairness as it is used to compare the achievements of more than one scientist. In particular, it often becomes difficult to quantify the achievement for each scientist if there are a lot of participants in the same research output. In this paper, a new nonlinear metrics model, called a credit function, is established to mine the information of the individual research outputs (IRO). An example is constructed to show that different credit functions may generate distinct ranking for the scientists. By the proposed nonlinear methods in this paper, the inequality relation of contribution in the same IRO can be quantified, and the obtained ranking on the scientists is more acceptable than the existing linear method available in the literature. Finally, the proposed metrics model is applied in solving three practical problems, especially combined with the technique for order preference by similarity to an ideal solution (TOPSIS).
In this paper, we delve into a group decision-making (GDM) approach based on incomplete linguistic interval-valued q-rung orthopair fuzzy preference relations (LIVq-ROFPRs), emphasizing the significance of consistency and consensus analysis. The LIVq-ROFPR is defined and the multiplicative consistency is further discussed by introducing the relevant lower and upper linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs). Taking into account the consistency level, two programming models are established. One aims at estimating the missing preference information, while the other is designed to rectify an unacceptably multiplicatively consistent LIVq-ROFPR. Utilizing the relationship between the normalized linguistic q-rung orthopair fuzzy priority weight vector and the multiplicatively consistent Lq-ROFPR, we develop a model for deriving the linguistic interval-valued q-rung orthopair fuzzy priority weights. Additionally, we introduce a group consensus index and determine decision-makers’ weights by minimizing this index. To reach an acceptable consensus level, we devise an iterative algorithm and calculate the adjustment parameter in each iteration step, which can theoretically guarantee a steady decrease of the group consensus index during the consensus improving process. Finally, we present two examples to illustrate the practical applications and advantages of our proposed GDM method.
In the current era, blockchain technology (BT) has emerged as a novel technique to maintain the operations of healthcare management systems. Assessment of blockchain technology (BT)-enabled hospitals can be considered as a multi-criteria decision making (MCDM) problem because of the existence of several criteria. The aim of this study is to develop a hybrid MCDM method for evaluating the factors of multi-criteria BT-enabled hospital selection problem under interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). For this purpose, a weighted aggregated sum product assessment (WASPAS) model is presented with the combination of IVq-ROF interaction aggregation operators, the standard deviation (SD)-based model and pivot pairwise relative criteria importance assessment (PIPRECIA) tool called IV-q-ROF-SD-PIPRECIA-WASPAS model within the context of IVq-ROFSs. For this purpose, some new IVq-ROF interaction aggregation operators are developed with their desirable characteristics. Next, the standard deviation-based model and PIPRECIA model on IVq-ROFSs are proposed to obtain the final weight of criteria, whereas the rank-based formula is presented to determine the decision experts’ weights with IVq-ROF information. The presented IV-q-ROF-SD-PIPRECIA-WASPAS model is applied on a case study of BT-enabled hospitals assessment, which confirms its applicability and usefulness. Sensitivity analysis and comparative discussion have been performed to reveal the consistency, robustness and efficiency of the presented model. The BT-enabled hospital-II with highest UD (0.4453) has emerged as the best choice among a set of BT-enabled hospitals. The factor "flexibilty" with highest weight (0.0898) value followed that the scalability (0.0809), transaction speed and accountability with same weight (0.0779) value, and network availability with weight (0.0771) for BT-enabled hospitals assessment. The final results conclude that the developed methodology can provide more accurate decisions while considering multiple indicators and input uncertainties.
Purpose: The article aims to identify changes in the intensity of large enterprises using modern technological solutions due to the regulations in force in the field of gaining digital sovereignty by implementing the European Digital Decade strategy. Design/methodology/approach: During the research process, data collected from Eurostat were compiled. They concerned the sector of large enterprises operating in the European Union in the years 2014-2022. The research procedure was carried out using the PCA and VIKOR methods, and the ICT dissemination index. Findings: The research results indicate that there are significant inequalities in the level of digitization and intensity of technology use among large enterprises. Entities located in Cyprus, Malta, Luxembourg, and Estonia have the greatest digital potential. In turn, the smallest technological resources were gathered by enterprises in France, Italy, Germany, Poland, and Spain. Based on the determined indicator of the dissemination of modern technologies, differences in the level of ICT implementation were found. Leaders in the implementation of modern technologies, i.e., Germany, France, and Estonia, were indicated. Research limitations/implications: Further research should focus on analyzing the use of technological resources for sustainable development, delays in the implementation of ICT technologies, the use of quantum technologies, and the levels of achieving digital sovereignty of entities. Practical implications: The research results provide business and state managers with information that can be used in the development and implementation of digital transformation strategies to increase digital potential and achieve digital sovereignty. Originality/value: The authors contribute to research on the digital transformation of large enterprises. They develop a technology diffusion index that provides information about the level of ICT use. Keywords: digital potential, ICT, Digital Compass, Europe's Digital Decade strategy. Category of the paper: Research paper.
Linguistic preference relations (LPRs) and its variations served for different decision-making situations are significantly important instruments of qualitative decision-making. The consistency analysis of LPRs is a necessary prerequisite for further operations of these original preference relations so as to ensure that the final decision results are convincing. However, the existing consistency improvement methods for LPRs are difficult to guarantee the reliability of the revised LPRs. Because the suggested LPRs from these methods either not eliminate the ordinal inconsistency or not satisfy the expectation of minimum modification. In this paper, a new definition of ordinal consistency of LPRs is first proposed and then an optimization approach is constructed to eliminate ordinal inconsistency for LPRs. Secondly, a new cardinal consistency index for LPRs is proposed and a corresponding optimization model to increase the cardinal consistency level is presented. After that, an optimization model is proposed to simultaneously manage ordinal and cardinal inconsistency for LPRs. Last, the proposed models are applied to a real linguistic decision-making problem involving evaluation and selection of investment projects. The comparative analysis and discussion illustrate the applicability and effectiveness of the proposed models.
This article aims to develop a novel hybrid multi‐attribute group decision‐making approach under interval‐valued intuitionistic fuzzy sets (IVIFS) by integrating variable weight, correlation coefficient, and technique for order performance by similarity to an ideal solution (TOPSIS). First, experts give their evaluation in IVIFS, and then the weighting evaluation matrix is computed based on interval‐valued intuitionistic fuzzy weighted averaging operator with the subjective attribute weights given in advance. Second, a simple and useful weighting approach on the basis of correlation coefficient is put forward to obtain the experts weights. Third, we treat the attribute weights as a varying vector, and then propose a variable weighting approach for its acquisition. Fourth, an individual decision can be converted to an alternative decision by considering the experts and attributes weights together. At last, the integrated assessment value of each alternative is computed by TOPSIS, and then the most appropriate alternative is chosen. Two illustrative examples dealt with the problem by the method presented in this article demonstrate the usefulness of this approach, compared with those by the other methods.
The multicriteria decision-making methodology is utilized to assess different portable hard disk drive alternatives, according to the purchaser/retailer/wholesaler liking with respect to various attributes. The hard disk drive comes under various types and has a number of attributes connected with it such as storage capacity, size, data transfer speed and physical dimensions. The modern market caters to a wide variety of customer needs. Therefore, it becomes the need of the hour to present a simple technique to select the best alternative for purchaser/retailer/wholesaler to satisfy their combined needs. Among the multicriteria decision-making methods, the more simple and widely used technique weighted aggregated sum product assessment is utilized in this work. The data of different hard disk drives were collected that were available in the Indian market and 24 different models of five brands were considered in decision-making. The equal weights method and objective weights method, that is standard deviation method, are utilized to allocate weights of significance to the criteria. The ranks obtained with simple additive weighting, weighted product method and weighted aggregated sum product assessment are presented, and final ranks are considered with weighted aggregated sum product assessment method because it is an amalgamation of the simple additive weighting and weighted product method. The result reveals that Western Digital comes out to be the first choice as a brand because the top three models belong to them with both equal and objective weights. While utilizing these techniques, a consumer can purchase the best hard disk drive and it is also very advantageous for merchants and sellers to aid users in procuring their gadgets while manufacture of hard disk drive can produce their product with unique technological features aimed at particular users. Furthermore, the subjective weights can be considered to select the best alternative.
This paper has built a EPC hydropower project risk index system based on the feature of EPC, which boasts complicated risk. It adopted the entropy method to determine the weight of risk evaluating indicators, and established the evaluation model based on the intuition uncertain linguistic term sets. Meanwhile, it constructed a comprehensive evaluation model based on equal risk curve and fuzzy theory to analyze the risk of the EPC contractor in an objective and scientific way. Finally, it gives a comprehensive evaluation of the EPC contractor's risk by applying it to real examples. According to the results, the model proves to be effective and feasible.
The power quality issues are challenging in microgrid due to the presence of various types of renewable energy resources unlike conventional power system. So, the main objective of this research is to quantify the power quality considering the fuzziness in variation of voltage, frequency, power factor and total harmonic distortion (THD) due to the occurrence of voltage sag, swell, interruption and unbalancing in three-phase AC microgrid feeding static and rotational loads. Therefore, a novel power quality monitoring index (PQMI) is proposed to determine the status of power quality. Total 256 numbers of rules are formed for fuzzy inference system (FIS) to assess PQMI considering the acceptable limits of above mentioned four input variables as per IEEE/IEC standards. The proposed methodology is verified through Mamdani and Sugeno type FIS using Matlab-Simulink software. It is also found that the proposed PQMI is significant to define the status of microgrid even during transition from grid-connected to islanded mode and vice-versa.
In this paper, we will discuss a mathematical modeling in determining the location of the transportation hub, so that the transportation hub can be placed optimally. In general, determining the location of the transportation hub is only considered the quantitative factors. However, in this paper will also consider the qualitative factor. Multi attribute group decision making (MAGDM) method will be used to bring qualitative forms into quantitative forms. This model is assumed that the number of passengers at a passenger generation point is unknown, therefore in this modeling there is a stochastic constraint. The distribution of the number of passengers in this paper is also unknown, therefore this modeling will be completed using nonparametric statistics estimation with generated data.
Investigating clusters of experts is an interesting topic in the large-group decision-making (LGDM) problem, since being familiar with patterns (groups) of experts is beneficial to some other actions needed for decision-making (e.g., reconciliation of opinions derived from different expert groups). However, not too much attention has been paid to expert clustering in the LGDM problem under a linguistic environment. Besides, it seems that only the decision information is utilized to group experts while the auxiliary (outside) knowledge (e.g., expertise and occupation) about these experts has not been fully considered during the clustering process. To address this issue, this study proposes a hybrid method integrating outside knowledge about experts with practical preference information under the interval-valued linguistic environment to cluster experts. The method consists of four elements: pre-clustering of experts according to the given knowledge, the optimization model to transform the interval-valued 2-tuple linguistic (IV2TL) decision information, the data envelopment analysis-discriminant analysis (DEA-DA) model to deal with a two-cluster issue, and iterative clustering based on the DEA-DA model to cluster experts into multiple clusters. The feasibility and validity of the proposed method are illustrated with a real-world example. A comparison with the maximal tree clustering method in the linguistic environment is provided.
Purpose
This paper aims to demonstrate how to make emergency decision when decision makers face a complex and turbulent environment that needs quite different decision-making processes from conventional ones. Traditional decision techniques cannot meet the demands of today’s social stability and security.
Design/methodology/approach
The main work is to develop an instance-driven classifier for the emergency categories based upon three fuzzy measures: features for an instance, solution for the instance and effect evaluation of the outcome. First, the information collected from the past emergency events is encodes into a prototype model. Second, a three-dimensional space that describes the locations and mutual distance relationships of the emergency events in different emergency prototypes is formulated. Third, for any new emergency event to be classified, the nearest emergency prototype is identified in the three-dimensional space and is classified into that category.
Findings
An instance-driven classifier based on prototype theory helps decision makers to describe emergency concept more clearly. The maximizing deviation model is constructed to determine the optimal relative weights of features according to the characteristics of the new instance, such that every customized feature space maximizes the influence of features shared by members of the category. Comparisons and discusses of the proposed method with other existing methods are given.
Practical implications
To reduce the affection to economic development, more and more countries have recognized the importance of emergency response solutions as an indispensable activity. In a new emergency instance, it is very challengeable for a decision maker to form a rational and feasible humanitarian aids scheme under the time pressure. After selecting a most suitable prototype, decision makers can learn most relevant experience and lessons in the emergency profile database and generate plan for the new instance. The proposed approach is to effectively make full use of inhomogeneous information in different types of resources and optimize resource allocation.
Originality/value
The combination of instances can reflect different aspects of a prototype. This feature solves the problem of insufficient learning data, which is a significant characteristic of emergency decision-making. It can be seen as a customized classification mechanism, while the previous classifiers always assume key features of a category.
This paper studies the ordinal and additive consistency issues of fuzzy linguistic preference relations (FLPRs). First, a graphic method of Gower plot is proposed to ascertain ordinal and additive inconsistencies for FLPRs. Then, two optimization models are established to adjust the ordinal and additive inconsistencies at the same time. Furthermore, an approach based on Gower plot is developed to help the decision maker to improve the consistency and rank the alternatives which respects the views of decision makers with greatest degree. Finally, numerical examples and comparisons with the existing methods are furnished to show the effectiveness and advantages of the proposed method.
The selection among renewable energy alternatives is a fuzzy multicriteria problem with many conflicting criteria under uncertainty. In many decision-making problems, the Decision Makers (DM) define their preference in linguistic form since it is relatively difficult to provide exact numerical values during the evaluation of alternatives. Therefore, in many studies, fuzzy logic is successfully used to model this kind of uncertainty. In this chapter, the authors try to capture this uncertainty by using interval type-2 fuzzy sets and hesitant fuzzy sets. They propose a fuzzy multicriteria method for the evaluation of renewable energy alternatives, in which the priority weights of the criteria are determined by interval type-2 fuzzy AHP, and the alternatives are ranked using hesitant fuzzy TOPSIS. A case study is also given.
The aim of this article is to investigate the approach for multi-attribute group decision-making, in which the attribute values take the form of multi-granularity multiplicative linguistic information. Firstly, to process multiple sources of decision information assessed in different multiplicative linguistic label sets, a method for transforming multi-granularity multiplicative linguistic information into multiplicative trapezoidal fuzzy numbers is proposed. Then, a formula for ranking multiplicative trapezoidal fuzzy numbers is given based on geometric mean. Furthermore, the concept of similarity degree between two multiplicative trapezoidal fuzzy numbers is defined. The attribute weights are obtained by solving some optimization models. An effective approach for group decision making with multi-granularity multiplicative linguistic information is developed based on the ordered weighted geometric mean operator and proposed formulae. Finally, a practical example is provided to illustrate the practicality and validity of the proposed method.
The hesitant fuzzy linguistic term sets(HFLTSs) can be used to represent an expert's hesitant preferences when assessing the membership of an element. By integrating the strength of HFLTSs in dealing with uncertainty and vagueness and the merit of grey relation analysis in modeling multi-criteria decision making, a gray relevance analysis method based on HFLTSs is proposed in this paper. The solving procedure is as follows, (i) the weights of criteria are determined by the group decision making models based on AHP; (ii) using the weighted grey relational degree between the reference data sequence and optimal data sequence to result the ranking order for all alternatives; (iii) An illustrative example is provided to verify the proposed approach and to demonstrate its practicality and effectiveness.
The cooling performance makes a full impact on the operation stability of the microcomputer chassis. Up to now, no effort is found toward on the experimental research of cooling performance of the microcomputer chassis cooled by forced convection. According to the operating temperature of CPU, graphics card and BGA, the cooling performance of a type of microcomputer is analyzed and optimized. Three fans are installed on the chassis, and they are inlet and outlet of the cooling air. Eight forced-convection heat-transfer schemes are developed by changing the operation state of three fans. The temperature of the inlet and outlet of the cooling air, the heat sinker of CPU, the heat sinker of graphics cards and the surface of BGA are tested using the thermocouple. Total heat-transfer ability, heat-transfer ability of CPU, graphics card and BGA are characterized by the temperature difference between inlet and outlet of cooling air, temperature difference between chip and heat sinker's edge of CPU and graphics card and the surface temperature of BGA, separately. Heat-transfer homogeneous of CPU, graphics card and BGA are characterized by temperature difference of heat sinker of CPU, graphics card and BGA. And then eight schemes are analyzed and optimized. The result shows that temperature difference of inlet and outlet of cooling air in No.2 scheme is largest, (3.0 °C), and the cooling air carries the most thermal power away. Temperature difference of CPU and graphics card in No.3 schemes are largest, (15.11 °C, 17.95 °C, separately), standard deviation is small, (0.309, 0.660, separately), and then the cooling performance of CPU and graphics card is best. Operating temperature of BGA in No.3 and No.4 schemes are lowest, (20.05 °C, 19.79 °C, separately), standard deviation is small, (0.687, 0.556, separately), and then the cooling performance of BGA is best. So take full account of cooling situation of CPU, graphics card and BGA, No.3 are the best forced-convection heat-transfer scheme of a type of microcomputer chassis. The proposed research provides a theoretical basis for forced-convection heat-transfer of microcomputer.
With the advent of the era of low-carbon economy, China enterprises urgently need for innovation in enterprises management if they want to occupy a place in the fierce market competition environment in the era of low-carbon economy, which puts forward the new requirements for energy conservation and emissions reduction to enterprises. To enterprises, promoting the management innovation under low carbon economy circumstances has the very vital significance, which can enhance the management ability and management level, and always possess a leading position in the market competition. In this paper, inspired by the method of traditional I-CG operator, we have proposed the induced hesitant fuzzy uncertain linguistic correlated geometric (IHFULCG) operator. Next, we exploited the IHFULCG operator to design some approaches to tackle the hesitant fuzzy uncertain linguistic multiple attribute decision making issues for evaluating the enterprise management innovation ability under low carbon economy circumstances. In the end, an example to estimate the enterprise management innovation ability under low carbon economy circumstances is given.
This paper presents consensus models based on distance for group decision making problems under interval fuzzy and multiplicative preference relations. First, some quadratic programming models based upon the idea of minimizing the sum of squared distances between all pairs of weighted interval fuzzy or multiplicative preference judgments are developed to obtain the weights of experts. Then, two indices, an individual to group consensus index (ICI) and a group consensus index (GCI) are defined. Furthermore, iterative consensus algorithms are proposed and the processes stop until both the ICI and GCI are less than predefined thresholds or reaching the maximum number of iteration. Finally, two illustrative examples are given to demonstrate the feasibility and effectiveness of the proposed methods.
Cloud computing technology has become increasingly popular and can deliver a host of benefits. However, there are various kinds of cloud providers in the market and firms need scientific decision tools to judge which cloud computing vendor should be chosen. Studies in how a firm should select an appropriate cloud vendor have just started. However, existing studies are mainly from the technology and cost perspective, and neglect other influence factors, such as competitive pressure and managerial skills, etc. Hence, this paper proposes a multi-attribute group decision-making (MAGDM) based scientific decision tool to help firms to judge which cloud computing vendor is more suitable for their need by considering more comprehensive influence factors. It is argued that objective attributes, i.e., cost, as well as subjective attributes, such as TOE factors (Technology, Organization, and Environment) should be considered for the decision making in cloud computing services, and presents a new subjective/objective integrated MAGDM approach for solving decision problems. The proposed approach integrates statistical variance (SV), improved techniques for order preference by similarity to an ideal solution (TOPSIS), simple additive weighting (SAW), and Delphi-AHP to determine the integrated weights of the attributes and decision-makers (DMs). The method considers both the objective weights of the attributes and DMs, as well as the subjective preferences of the DMs and their identity differences, thereby making the decision results more accurate and theoretically reasonable. A numerical example is given to illustrate the practicability and usefulness of the approach and its suitability as a decision-making tool for a firm using of cloud computing services. This paper enriches the theory and methodology of the selection problem of cloud computing vendoring and MAGDM analysis.
多属性决策（或称之为有限个方案的多目标决策）是现代决策科学的一个重要组成部分，
它的理论和方法在工程设计、经济、管理和军事等诸多领域中有着广泛的应用，如：投资决
策、项目评估、工厂选址、投标招标、维修服务、武器系统性能评定、产业部门发展排序以及经
济效益综合评价等．近年来，由于客观事物的复杂性、不确定性以及人类思维的模糊性，对不
确定环境下的多属性决策问题研究已引起人们的极大关注．本书将介绍不确定多属性决策
（包括不确定多属性群决策）方法及其在供应链管理、风险投资、教师质量评定、干部选拔、产
品改造和虚拟企业领域中的合作伙伴选择等诸多方面的应用．本书可作为高等院校运筹学、
管理科学、信息科学和系统工程专业的高年级本科生和研究生教材，并可作为工程技术人员、
管理干部、教师以及有关方面学者的参考书．
A problem that we had encountered in the aggregation process, is how to aggregate the elements that have cardinality >1. The purpose of this article is to present a new aggregation operator of linguistic labels that uses the cardinality of these elements, the linguistic aggregation of majority additive (LAMA) operator. We also present an extension of the LAMA operator under the two-tuple fuzzy linguistic representation model. © 2003 Wiley Periodicals, Inc.
The multi-attribute decision making problems are studied, in which the information about the attribute values take the form of uncertain linguistic variables. The concept of deviation degree between uncertain linguistic variables is defined, and ideal point of uncertain linguistic decision making matrix is also defined. A formula of possibility degree for the comparison between uncertain linguistic variables is proposed. Based on the deviation degree and ideal point of uncertain linguistic variables, an optimization model is established, by solving the model, a simple and exact formula is derived to determine the attribute weights where the information about the attribute weights is completely unknown. For the information about the attribute weights is partly known, another optimization model is established to determine the weights, and then to aggregate the given uncertain linguistic decision information, respectively. A method based on possibility degree is given to rank the alternatives. Finally, an illustrative example is also given.
In those problems that deal with multiple sources of linguistic
information we can find problems defined in contexts where the
linguistic assessments are assessed in linguistic term sets with
different granularity of uncertainty and/or semantics (multigranular
linguistic contexts). Different approaches have been developed to manage
this type of contexts, that unify the multigranular linguistic
information in an unique linguistic term set for an easy management of
the information. This normalization process can produce a loss of
information and hence a lack of precision in the final results. In this
paper, we shall present a type of multigranular linguistic contexts we
shall call linguistic hierarchies term sets, such that, when we deal
with multigranular linguistic information assessed in these structures
we can unify the information assessed in them without loss of
information. To do so, we shall use the 2-tuple linguistic
representation model. Afterwards we shall develop a linguistic decision
model dealing with multigranular linguistic contexts and apply it to a
multi-expert decision-making problem
The fuzzy linguistic approach has been applied successfully to
many problems. However, there is a limitation of this approach imposed
by its information representation model and the computation methods used
when fusion processes are performed on linguistic values. This
limitation is the loss of information; this loss of information implies
a lack of precision in the final results from the fusion of linguistic
information. In this paper, we present tools for overcoming this
limitation. The linguistic information is expressed by means of
2-tuples, which are composed of a linguistic term and a numeric value
assessed in (-0.5, 0.5). This model allows a continuous representation
of the linguistic information on its domain, therefore, it can represent
any counting of information obtained in a aggregation process. We then
develop a computational technique for computing with words without any
loss of information. Finally, different classical aggregation operators
are extended to deal with the 2-tuple linguistic model
By hot-pressing method, TiB2-TiC multiphase ceramics were fabricated from TiB2-TiC composites powders under the following sintering conditions: sintering temperature at 1700°C and 1800°C, pressure at 30 MPa, sintering time for 60 min. The relative density, the hardness and fracture toughness of TiB2-TiC multiphase ceramic at room temperature were 99.8%, 93.2 HRA and 5.53 MPa · m1/2 respectively. The residual porosities and dislocation in sintered ceramics went against the performance. The microstructure of TiB2-TiC multiphase ceramics from composite powders had smaller and more symmetrical grains than the TiB2-TiC ceramics sintered from the mixtures of TiB2 and TiG powders. The elements of B, C and Ti at the interface of TiB2 and TiC were distributed gradually. There were no impurities at the interface and the bonds between phases were strong, which probably has relation to the higher properties of TiB2-TiC multiphase ceramics. The growth of TiB2 in different crystal directions was different in TiB2-TiC multiphase ceramics.
Binary relations play a central role in various fields of mathematics. Especially, equivalence relations and different kinds of ordering relations are employed in basic mathematical models. Typical areas are decision making and measurement theory. In addition, applications of binary relations appear naturally in social sciences.
This paper proposes a fuzzy group decision making (FGDM) approach for bridge risk assessment. The FGDM approach allows decision makers (DMs) to evaluate bridge risk factors using linguistic terms such as Certain, Very High, High, Slightly High, Medium, Slightly Low, Low, Very Low or None rather than precise numerical values, allows them to express their opinions independently, and also provides two alternative algorithms to aggregate the assessments of multiple bridge risk factors, one of which offers a rapid assessment and the other one leads to an exact assessment. A case study is investigated using the FGDM approach to illustrate its applications in bridge risk assessment. It is shown that the FGDM approach offers a flexible, practical and effective way of modelling bridge risks.
A MADM problem is given as: {\underset{\raise0.3em\hbox{}}{w}} = ({{w}_{1}},{{w}_{2}}, \ldots ,{{w}_{n}}) where Ai, i = 1, ..., m, are possible courses of action (candidates, alternatives); Xj, j = 1,...,n, are attributes with which alternative performances are measured; xij is the performance score (or rating) of alternative Ai with respect to attribute Xj; wj, j = 1,...,n are the relative importance of attributes.
This article is devoted to defining some aggregation operations between linguistic labels. First, from some remarks about the meaning of label addition, a formal and general definition of a label space is introduced. After, addition, difference, and product by a positive real number are formally defined on that space. the more important properties of these operations are studied, paying special attention to the convex combination labels. the article concludes with some numerical examples. © 1993 John Wiley Sons, Inc.
After arguing that in the knowledge acquisition framework experts can not always supply a precise semantics for the linguistic labels they use, we show that negation functions over an ordered set of linguistics labels induce a semantics. We study the semantics induced by classical negation, functions from L to L, and also the one induced by negation functions from L to parts of L.
—We are primarily concerned with the problem of aggregating multicriteria to form an overall decision function. We introduce a new type of operator for aggregation called an ordered weighted aggregation (OWA) operator. We investigate the properties of this operator. We particularly see that it has the property of lying between the “and,” requiring all the criteria to be satisfied, and the “or,” requiring at least one of the criteria to be satisfied. We see these new OWA operators as some new family of mean operators.
The aim of this paper is to put forward a method for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. An aggregating operator named linguistic weighted arithmetic averaging (LWAA) operator is introduced to aggregate the given decision information to get the overall preference value of each alternative. Some properties of the LWAA operator are also investigated. Based on the idea that the attribute with a larger deviation value among alternatives should be evaluated a larger weight, a method to determine the optimal weighting vector of LWAA operator is developed under the assumption that attribute weights are completely unknown. The based approach is extended to the situation where partially weight information can be obtained by solving a constrained non-linear optimization problem. Then a procedure to group multiple attribute decision making is provided under linguistic environment. Finally, an example of risk investment problem is given to verify the proposed approach; a comparative study to fuzzy ordered weighted averaging (F-OWA) operator methods is also demonstrated.
The multi-attribute decision making problems are studied, in which the information about the attribute values take the form of uncertain linguistic variables. The concept of deviation degree between uncertain linguistic variables is defined, and ideal point of uncertain linguistic decision making matrix is also defined. A formula of possibility degree for the comparison between uncertain linguistic variables is proposed. Based on the deviation degree and ideal point of uncertain linguistic variables, an optimization model is established, by solving the model, a simple and exact formula is derived to determine the attribute weights where the information about the attribute weights is completely unknown. For the information about the attribute weights is partly known, another optimization model is established to determine the weights, and then to aggregate the given uncertain linguistic decision information, respectively. A method based on possibility degree is given to rank the alternatives. Finally, an illustrative example is also given.
In this paper, two uncertain linguistic aggregation operators called uncertain linguistic ordered weighted averaging (ULOWA) operator and uncertain linguistic hybrid aggregation (ULHA) operator are proposed. An approach to multiple attribute group decision making with uncertain linguistic information is developed based on the ULOWA and the ULHA operators. Finally, a practical application of the developed approach to the problem of evaluating university faculty for tenure and promotion is given.
This paper deals with the problem of linguistic approximation in a computerized system the context of medical decision making. The general problem and a few application-oriented solutions have been treated in the literature. After a review of the main approaches (best fit, successive approximations, piecewise decomposition, preference set, fuzzy chopping) some of the unresolved problems are pointed out. The case of deciding upon various diagnostic abnormalities suggested by the analysis of the electrocardiographic signal is then put forward. The linguistic approximation method used in this situation is finally described. Its main merit is its simple (i.e., easily understood) linguistic output, which uses labels whose meaning is rather well established among the users (i.e., the physicians).
This paper proposes a fuzzy TOPSIS method based on alpha level sets and presents a nonlinear programming (NLP) solution procedure. The relationship between the fuzzy TOPSIS method and fuzzy weighted average (FWA) is also discussed. Three numerical examples including an application to bridge risk assessment are investigated using the proposed fuzzy TOPSIS method to illustrate its applications and the differences from the other procedures. It is shown that the proposed fuzzy TOPSIS method performs better than the other fuzzy versions of the TOPSIS method.
In this paper, we study the group decision making problem with linguistic preference relations. We first show that the weighted combination of A1,A2,…,Am is linguistic preference relation under the condition that all of A1,A2,…,Am are linguistic preference relations. Then we define the concepts of deviation degree and similarity degree between two linguistic values, and deviation degree and similarity degree between two linguistic preference relations. We also show that the deviation degree between linguistic preference relation Ai of A1,A2,…,Am and their group linguistic preference relation is no greater than the largest deviation degree between the linguistic preference relation Ai and each of the linguistic preference relations A1,A2,…,Am. Thus, a theoretic basis has been established for the application of linguistic preference relations in group decision making.
The ordered weighted averaging (OWA) operator was developed by Yager [IEEE Trans. Syst., Man, Cybernet. 18 (1998) 183]. Later, Yager and Filev [IEEE Trans. Syst., Man, Cybernet.––Part B 29 (1999) 141] introduced a more general class of OWA operators called the induced ordered weighted averaging (IOWA) operators, which take as their argument pairs, called OWA pairs, in which one component is used to induce an ordering over the second components which are exact numerical values and then aggregated. The aim of this paper is to develop some induced uncertain linguistic OWA (IULOWA) operators, in which the second components are uncertain linguistic variables. Some desirable properties of the IULOWA operators are studied, and then, the IULOWA operators are applied to group decision making with uncertain linguistic information.
In this paper, we define some operational laws of linguistic variables and develop some new aggregation operators such as linguistic geometric averaging (LGA) operator, linguistic weighted geometric averaging (LWGA) operator, linguistic ordered weighted geometric averaging (LOWGA) operator and linguistic hybrid geometric averaging (LHGA) operator, etc., which can be utilized to aggregate preference information taking the form of linguistic variables, and then study some desirable properties of the operators. Based on the LGA and the LHGA operators, we propose a practical method for group decision making with linguistic preference relations. The method is straightforward and has no loss of information. Finally, an illustrative numerical example is also given.
The normalization of interval and fuzzy weights is often necessary in multiple criteria decision analysis (MCDA) under uncertainty, especially in analytic hierarchy process (AHP) with interval or fuzzy judgements. The existing normalization methods based on interval arithmetic and fuzzy arithmetic are found flawed and need to be revised. This paper presents the correct normalization methods for interval and fuzzy weights and offers relevant theorems in support of them. Numerical examples are examined to show the correctness of the proposed normalization methods and their differences from those existing normalization methods.
The problem of finding a solution set of alternatives when a linguistic preference relation represents a collective preference is analyzed following two research lines, choice functions and mechanisms.Four classical choice sets of alternatives for a linguistic preference relation are presented and some relations between them are pointed out. The concept of linguistic choice function as a tool to derive linguistic choice sets of alternatives is introduced and some particular linguistic choice functions are presented together with a study of their rationality properties. On the other hand, two types of linguistic choice mechanisms to derive solution sets of alternatives from linguistic choice functions are introduced: simple and composite ones.The concept of linguistic covering relation is introduced with a view to allow us the design of consistent linguistic choice mechanisms which may achieve more precise and coherent solution sets of alternatives.
A study on the steps to follow in linguistic decision analysis is presented in a context of multi-criteria/multi-person decision making. Three steps are established for solving a multi-criteria decision making problem under linguistic information: (i) the choice of the linguistic term set with its semantic in order to express the linguistic performance values according to all the criteria, (ii) the choice of the aggregation operator of linguistic information in order to aggregate the linguistic performance values, and (iii) the choice of the best alternatives, which is made up by two phases: (a) the aggregation of linguistic information for obtaining a collective linguistic performance value on the alternatives, and (b) the exploitation of the collective linguistic performance value in order to establish a rank ordering among the alternatives for choosing the best alternatives. Finally, an example is shown.
In a linguistic framework, several group decision making processes by direct approach are presented. These processes are designed using the linguistic ordered weighted averaging (LOWA) operator. To do so, first a study is made of the properties and the axiomatic of LOWA operator, showing the rationality of its aggregation way. And secondly, we present the use of LOWA operator to solve group decision making problems from individuals linguistic preference relations.
This paper revisits the fuzzy logarithmic least squares method (LLSM) in the analytic hierarchy process and points out its incorrectness in the normalization of local fuzzy weights, infeasibility in deriving the local fuzzy weights of a fuzzy comparison matrix when the lower bound value of a non-normalized fuzzy weight turns out to be greater than its upper bound value, uncertainty of local fuzzy weights for incomplete fuzzy comparison matrices, and unreality of global fuzzy weights. A modified fuzzy LLSM, which is formulated as a constrained nonlinear optimization model, is therefore suggested to tackle all these problems. A numerical example is examined to show the applicability of the modified fuzzy LLSM and its advantages.
The aim of this paper is to extend the TOPSIS to the fuzzy environment. Owing to vague concepts frequently represented in decision data, the crisp value are inadequate to model real-life situations. In this paper, the rating of each alternative and the weight of each criterion are described by linguistic terms which can be expressed in triangular fuzzy numbers. Then, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the concept of the TOPSIS, a closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS) simultaneously. Finally, an example is shown to highlight the procedure of the proposed method at the end of this paper.
In this paper, a sequential selection process in group decision making under linguistic assessments is presented, where a set of linguistic preference relations represents individuals preferences. A collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority, specified by a fuzzy linguistic quantifier. Then we define the concepts of linguistic non-dominance, linguistic dominance, and strict dominance degrees as parts of the sequential selection process. The solution alternative(s) is obtained by applying these concepts.
The aim of this paper is to investigate the multiple attribute decision making problems with linguistic information, in which the information about attribute weights is incompletely known, and the attribute values take the form of linguistic variables. We first introduce some approaches to obtaining the weight information of attributes, and then establish an optimization model based on the ideal point of attribute values, by which the attribute weights can be determined. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. We utilize the numerical weighting linguistic average (NWLA) operator to aggregate the linguistic variables corresponding to each alternative, and then rank the alternatives by means of the aggregated linguistic information. Finally, the developed method is applied to the ranking and selection of propulsion/manoeuvring system of a double-ended passenger ferry.
This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the α-cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the α-cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the α-cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration.
Within the frame of decision aid literature, decision making problems with multiple sources of information have drawn the attention of researchers from a wide spectrum of disciplines. In decision situations with multiple individuals, each one has his own knowledge on the alternatives of the decision problem. The use of information assessed in different domains is not a seldom situation. This non-homogeneous information can be represented as values belonging to domains with different nature as linguistic, numerical and interval valued or can be values assessed in label sets with different granularity, multi-granular linguistic information. Decision processes for solving these problems are composed by two phases: aggregation and exploitation. The main problem to deal with non-homogeneous contexts is how to aggregate the information assessed in these contexts? In this paper, taking as base the 2-tuple fuzzy linguistic representation model we shall develop an aggregation process for dealing with non-homogeneous contexts. In first place, we shall develop an aggregation process for combining numerical, interval valued and linguistic information, afterwards we shall propose different extensions of this process to deal with contexts in which can appear other type of information as intuitionistic fuzzy sets or multi-granular linguistic information. � 2004 Elsevier B.V. All rights reserved.
In this paper, we define the concept of uncertain multiplicative linguistic preference relation, and introduce some operational laws of uncertain multiplicative linguistic variables. We propose some new aggregation operators including the uncertain linguistic geometric mean (ULGM) operator, uncertain linguistic weighted geometric mean (ULWGM) operator, uncertain linguistic ordered weighted geometric (ULOWG) operator, and induced uncertain linguistic ordered weighted geometric (IULOWG) operator. The IULOWG operator is a more general type of aggregation operator, which is based on the ULGM and ULOWG operators. Moreover, based on the ULOWG and IULOWG operators and the formula for the comparison between two uncertain multiplicative linguistic variables, we develop an approach to group decision making with uncertain multiplicative linguistic preference relations, and, finally, an application of the approach to group decision-making problem with uncertain multiplicative linguistic preference relations is pointed out.
We are primarily concerned with the problem of aggregating multicriteria to form an overall decision function. We introduce a new type of operator for aggregation called an ordered weighted aggregation (OWA) operator. We investigate the properties of this operator. We particularly see that it has the property of lying between the “and,” requiring all the criteria to be satisfied, and the “or,” requiring at least one of the criteria to be satisfied. We see these new OWA operators as some new family of mean operators.
The aim of this paper is to present a fusion approach of multi-granularity linguistic information for managing information assessed in different linguistic term sets (multigranularity linguistic term sets) together with its application in a decision making problem with multiple information sources, assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and/or semantic. In this context, a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives. First, the fusion of the multi-granularity linguistic performance values is carried out in order to obtain collective performance evaluations. In this step, on the one hand, the multi-granularity linguistic information is made uniform using a linguistic term set as the uniform representation base, the basic linguistic term set. On the other hand, the collective performance evaluations of ...
A method based on standard and mean deviations for determining the weight coefficients of multiple attributes and its applications
- Y M Wang
Wang, Y. M. (2003). A method based on standard and mean deviations for determining the weight coefficients of multiple attributes and its applications. Mathematical Statistics and Management, 22, 22–26.
On the normalization of internal and fuzzy weights. Fuzzy Sets and System. v157
- Elhag Wang