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Evaluation of Online Education Software Under Neutrosophic Environment
Abstract
Nowadays, the online learning system is developing in higher education. There are several causes this occurs, including pandemic restrictions, flexible access to content and instruction at any place, and cost-effectiveness for education institutions. Online learning can also enhance the availability of learning experiences for scholars. For this reason, several options must be evaluated for online educators. The goal is to highlight what factors students find essential in guaranteeing quality learning outcomes in the online learning environment. Therefore, we detected evaluation criteria including qualitative factors, and we used neutrosophic sets, which is a generalization of classic set, to deal with imprecise data with qualitative factors. In this chapter, for this aim, we propose the neutrosophic MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form) method to evaluate online learning software concerning some critical factors which have an essential influence on student satisfaction. For the validity of the proposed method, we also present comparative and sensitivity analyses. Finally, we performed a comparison analysis with neutrosophic TOPSIS method.
... According to the findings, there is a positive connection between academic achievement and gross domestic product (GDP), whereas there is a negative connection between academic achievement and infant mortality. The neutrosophic MULTIMOORA approach was introduced by Kutlu and Aydan [20] as a means of evaluating online learning software in relation to several crucial aspects that have a substantial impact on the level of satisfaction experienced by students. The purpose of their research is to draw attention to the variables that students believe are most important to ensure that the results of their online education are of good quality. ...
There is evidence that students feel less involved in distance learning, which needs more work from their educators. While distance education allows learners to feel less reluctant andor timid to ask questions, there is also evidence that students feel less interested in distance education. Students may obtain information and knowledge at their own pace and convenience via the use of distance education. Also, it may assist in reaching the same overall performance and ultimate score as would be achieved via face-to-face instruction. The goal of this study analyzes the performance of video conferences in smart learning. This analysis contains many criteria, so the concept of multi-criteria decision-making is integrated with the neutrosophic sets to overcome uncertain information. We used the neutrosophic AHP to show the importance of each criterion. There are seven criteria used in this paper. The findings demonstrated that the utilisation of video conferences enabled students to gain access to information and educational resources, had a positive effect on the students' constructing knowledge and critical reflection, and resulted in the students reporting an extremely positive learning experience in the context of smart learning.
The dynamic requirements of the learners are redefining the process of teaching and learning and keeping the processes in the state of transience. The learning shall be made more effective by the right choice of the teaching method and it is necessary for every teaching method to possess certain essential attributes of flexibility, time efficiency, learner centeredness, and many other attributes. In this chapter, a decision-making problem with five criteria and eight alternatives of teaching methods is considered and the method of neutrosophic TOPSIS (technique for order preference by similarity to ideal solution) is applied to find the optimal ranking of the methods. In this research work the notion of single valued neutrosophic set with linguistic components is introduced as a means of making decision process more pragmatic, realistic, and feasible. This extended notion will certainly set a paradigm shift in decision making with linguistic representations.
The paper’s aims are to present a novel concept of linguistic interval-valued Pythagorean fuzzy set (LIVPFS) or called a linguistic interval-valued intuitionistic type-2 fuzzy set, which is a robust and trustworthy tool, and to accomplish the imprecise information while solving the decision-making problems. The presented LIVPFS is a generalization of the linguistic Pythagorean fuzzy set, by characterizing the membership and non-membership degrees as the interval-valued linguistic terms to represent the uncertain information. To explore the study, we firstly define some basic operational rules, score and accuracy functions, and the ordering relations of LIVPFS with a brief study of the desirable properties. Based on the stated operational laws, we proposed several weighted averages and geometric aggregating operators to aggregate the linguistic interval-valued Pythagorean fuzzy information. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Finally, a multiple attribute group decision-making (MAGDM) algorithm is promoted to solve the group decision-making problems with uncertain information using linguistic features and the proposed operators. The fundamental inequalities between the proposed operators and their properties are discussed in detail. Also, the illustration of the stated algorithm is given through several numerical examples and compared their performance with the results of the existing algorithms. Based on the stated MAGDM algorithm and the suitable operators, the decision-makers’ can be selected their best alternatives with their own attitude character towards optimism or pessimism choice. The presented LIVPFS is an extension of the several existing sets and is more generalized to utilize the uncertain and imprecise information with a wider range of information. Based on the presented aggregation operators, a decision-maker can select the desired one as per their choices to access the finest alternatives.
The foremost broadly utilized strategy for the valuation of the overall performance of a set of identical decision-making units (DMUs) that use analogous sources to yield related outputs is data envelopment analysis (DEA). However, the witnessed values of the symmetry or asymmetry of different types of information in real-world applications are sometimes inaccurate, ambiguous, inadequate, and inconsistent, so overlooking these conditions may lead to erroneous decision-making. Neutrosophic set theory can handle these occasions of data and makes an imitation of the decision-making procedure with the aid of thinking about all perspectives of the decision. In this paper, we introduce a model of DEA in the context of neutrosophic sets and sketch an innovative process to solve it. Furthermore, we deal with the problem of healthcare system evaluation with inconsistent, indeterminate, and incomplete information using the new model. The triangular single-valued neutrosophic numbers are also employed to deal with the mentioned data, and the proposed method is utilized in the assessment of 13 hospitals of Tehran University of Medical Sciences of Iran. The results exhibit the usefulness of the suggested approach and point out that the model has practical outcomes for decision-makers.
Single-valued neutrosophic numbers (SVN-numbers) are a special kind of neutrosophic set on the real number set. The concept of a SVN-number is important for quantifying an ill-known quantity and ranking of SVN-number is a very difficult situation in decision-making problems. The main aim of this paper is to present a new ranking methodology of SVN-numbers for solving multi-attribute decision-making problems. Therefore, we firstly define the possibility mean, variance and standard deviation of single-valued neutrosophic numbers. Using the ratio of possibility mean and standard deviation, we have developed the proposed ranking approach and applied to MADM problems. Finally, a numerical example is examined to show the applicability and embodiment of the proposed method.
: Passenger satisfaction is an important factor that affects the choice of travel modes for municipalities, especially in big cities. This evaluation is an important task for managers when they are considering improving the competitiveness of the public transportation system. However, passenger satisfaction evaluation is difficult as the information provided by passengers is often vague, imprecise, and uncertain. This paper aims to propose a new method, using Pythagorean fuzzy sets and multi-objective optimization by a ratio analysis plus full multiplicative form method (MULTIMOORA), to evaluate the passenger satisfaction level of the public transportation system under large group environment. The former is employed to represent the satisfaction assessments of rail transit network provided by passengers. The latter is extended and used to determine the passenger satisfaction levels of rail transit lines. In addition, a combination weighting method is suggested to compute the relative weights of evaluation criteria. A case study of the rail transit network in Shanghai is provided to demonstrate the effectiveness of the proposed passenger satisfaction evaluation method. The result shows that the new method proposed in this study can not only model passengers’ satisfaction evaluation information with more uncertainties, but also determine more reasonable and credible satisfaction levels of rail transit lines.
In the present paper, for first time, a System of Neutrosophic Linear Equations (SNLE) is
investigated based on the embedding approach. To this end, the (,,)-cut is used for
transformation of SNLE into a crisp linear system. Furthermore, the existence of a neutrosophic
solution to n x n linear system is proved in details and a computational procedure for solving the
SNLE is designed. Finally, numerical experiments are presented to show the reliability and
efficiency of the method.
Data envelopment analysis (DEA) is one of the best mathematical techniques to compute the overall
performance of units with some inputs and outputs. The original DEA methods are developed to tackle the information
based on the crisp number but no ability to handle the indeterminacy, impreciseness, vagueness, inconsistent, and
incompleteness information such as triangular neutrosophic numbers (TNNs). This study attempts to establish a new
model of DEA, where the information on decision-making units is TNNs. Initially, the concept and features of a
conventional DEA model and the comparative TNNs are discussed. Besides, some new ranking functions of TNNs are
presented. Furthermore, based on the mentioned ranking functions, an algorithm for solving the new model has been
established. A comparison of the new model with an existing method and other kinds of uncertainty tools has been
provided. In comparison with the existing methods, the significant characteristic of the new model is that it can handle
the triangular neutrosophic information simply and effectively. Finally, the implementation of this strategy for an
example has been applied for various models of DEA.
Single valued neutrosophic (SVN) set has a useful independent mathematical structure for expressing the incomplete, inconsistent and indeterminate information. Many researchers have studied decision making problems with SVN environment. This paper presented a new ranking method of SVN-numbers based on possibility theory for solving a multi-attribute decision making (MADM) problem. The first time we have defined the concept of possibility mean of SVN numbers and applied to multi-attribute decision making problem in which the attribute values are considered as SVN-numbers. Then, we propose the possibility mean of the truth-membership function, indeterminacy-membership function and falsity-membership function for single valued trapezoidal neutrosophic (SVTN) numbers and studied some desired properties of SVTN. Thus, we have developed a new ranking approach using the concept of weighted possibility mean, and applied to MADM problems. Finally, a numerical example is examined to show the applicability and an embodiment of the proposed method.
The paper aims to give some new kinds of operational laws named as neutrality addition and scalar multiplication for the pairs of single-valued neutrosophic numbers. The main idea behind these operations is to include the neutral characters of the decision-maker towards the preferences of the objects when it shows the equal degrees to membership functions. Some salient features of them are investigated also. Further based on these laws, some new aggregation operators are developed to aggregate the different preferences of the decision-makers. Desirable relations and properties are investigated in detail. Finally, a multiattribute group decision-making approach based on the proposed operators is presented and investigated with numerous numerical examples. The superiors, as well as the advantages of the operators, are also discussed in it.
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.
Mining method selection (MMS) is one of the core contents in mining design. As the influencing factors of MMS are in general of ambiguity or uncertainty, MMS can therefore be deemed as a complex fuzzy multi-criteria decision making problem. To resolve this problem, an extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach is studied in this paper. Three major contributions of this study are included. At first, comparative importance is crisp number in most stepwise weight assessment ratio analysis (SWARA) method, while linguistic terms are utilized to determine the criteria weights in the improved SWARA. Then, several Heronian mean (HM) operators related to linguistic neutrosophic numbers (LNNs) are defined to cope with evaluating indicators’ interrelations. Special cases are discussed, and primary properties are proved as well. At last, in combination with improved SWARA and HM operators, a novel decision making method, extended MULTIMOORA approach based on LNNs, is proposed. Applying this new approach to selecting the optimal mining method through an example, the feasibility is indicated. In addition, analyses of the strengths of the presented method are performed in comparison with other existing approaches.
Failure mode and effect analysis (FMEA) is a prospective risk assessment tool used to identify, assess and eliminate potential failure modes in various industries to improve security and reliability. However, the conventional risk priority number (RPN) method has been widely criticized for the deficiencies in risk factor weights, calculation of RPN, evaluation of failure modes, etc. In this paper, we present a novel approach for FMEA based on interval-valued intuitionistic fuzzy sets (IVIFSs) and MULTIMOORA method to handle the uncertainty and vagueness from FMEA team members’ subjective assessments and to get a more accurate ranking of failure modes identified in FMEA. In this proposed model, interval-valued intuitionistic fuzzy (IVIF) continuous weighted entropy is applied for risk factor weighting and the IVIF-MULTIMOORA method is used to determine the risk priority order of failure modes. Finally, an illustrative case is provided to demonstrate the effectiveness and practicality of the proposed FMEA and a comparison analysis with other relevant methods is conducted to show its merits.
Many real-world decision-making problems are complex and placed in a fuzzy environment, especially when it is related to predictions and assessments. Therefore, an extension of the MULTIMOORA method, primarily adapted for the use of interval-valued triangular fuzzy numbers as well as the use of the group decision-making approach and linguistic variables, is proposed in this paper. In order to demonstrate the applicability and effectiveness of the proposed approach, an example of comminution circuits design selection is considered.
The paper introduces the concept of simplified neutrosophic sets (SNSs), which are a subclass of neutrosophic sets, and defines the operational laws of SNSs. Then, we propose some aggregation operators, including a simplified neutrosophic weighted arithmetic average operator and a simplified neutrosophic weighted geometric average operator. Based on the two aggregation operators and cosine similarity measure for SNSs, a multicriteria decision-making method is established in which the evaluation values of alternatives with respective to criteria are represented by the form of SNSs. The ranking order of alternatives is performed through the cosine similarity measure between an alternative and the ideal alternative and the best one(s) can be determined as well. Finally, a numerical example shows the application of the proposed method.
Multiple criteria decision making methods have received different extensions under the uncertain environment in recent years. The aim of the current research is to extend the application of the MULTIMOORA method (Multiobjective Optimization by Ratio Analysis plus Full Multiplicative Form) for group decision making in the uncertain environment. Taking into account the advantages of IVIFS (interval-valued intuitionistic fuzzy sets) in handling the problem of uncertainty, the development of the interval-valued intuitionistic fuzzy MULTIMOORA (IVIF-MULTIMOORA) method for group decision making is considered in the paper. Two numerical examples of real-world civil engineering problems are presented, and ranking of the alternatives based on the suggested method is described. The results are then compared to the rankings yielded by some other methods of decision making with IVIF information. The comparison has shown the conformity of the proposed IVIF-MULTIMOORA method with other approaches. The proposed algorithm is favorable because of the abilities of IVIFS to be used for imagination of uncertainty and the MULTIMOORA method to consider three different viewpoints in analyzing engineering decision alternatives.
Health-care waste (HCW) management is a high priority public health and environmental concern particularly in developing countries. The decision to select an optimal technology for the disposal of HCW is a complicated multi-criteria decision analysis problem involving both qualitative and quantitative factors. Evaluating HCW treatment technologies may be based on imprecise information or uncertain data. Moreover, there can be significant dependence and feedbacks between the different dimensions and criteria. However, most existing decision models for HCW cannot capture these complex interrelationships. In response, this paper proposes a novel hybrid multi-criteria decision making (MCDM) model by integrating the 2-tuple DEMATEL technique and fuzzy MULTIMOORA method for selection of HCW treatment alternatives. It makes use of modified 2-tuple DEMATEL for obtaining the relative weights of criteria and fuzzy MULTIMOORA for assessing the alternatives according to each criterion. Specifically, an empirical case in Shanghai, one of the largest cities in China, is provided to illustrate the potential of the new model. Results show that the proposed framework for evaluating HCW treatment technologies is effective and provides meaningful implications for engineering designers to refer.
In order to determine the membership of an element to a set owing to ambiguity between a few different values, the hesitant fuzzy set (HFS) has been proposed and widely diffused to deal with vagueness and uncertainty involved in the process of multiple criteria group decision making (MCGDM) problems. In this paper, we develop novel definitions of score function and distance measure for HFSs. Some examples are given to illustrate that the proposed definitions are more reasonable than the traditional ones. Furthermore, our study extends the MULTIMOORA (Multiple Objective Optimization on the basis of Ratio Analysis plus Full Multiplicative Form) method with HFSs. The proposed method thus provides the means for multiple criteria decision making (MCDM) regarding uncertain assessments. Utilization of hesitant fuzzy power aggregation operators also enables facilitating the process of MCGDM. A numerical example of software selection demonstrates the possibilities of application of the proposed method.
This paper aims to extend fuzzy MULTIMOORA with linguistic reasoning and group decision-making (MULTIMOORA-FG). The new method consists of the three parts, namely the fuzzy Ratio System, the fuzzy Utopian Reference Point, and the fuzzy Full Multiplica-tive Form offering a robust comparison of alternatives against multiple objectives. In addition, MULTIMOORA-FG is designed to deal with triangular fuzzy numbers which, in turn, can resem-ble linguistic variables. MULTIMOORA-FG is a proper instrument for linguistic reasoning under fuzzy environment. In our study an application of personnel selection illustrates the group decision-making procedure according to MULTIMOORA-FG. Given the uncertainties peculiar of personnel selection, the application of multi-objective decision making (MODM) is required in this area. Fuzzy MULTIMOORA enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform a more robust personnel selection. The committee decided to consider eight qualitative characteristics expressed in linguistic variables. A numerical exam-ple exhibited possibilities for improvement of human resources management or any other business decision-making by applying MULTIMOORA-FG.
Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the set-theoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.
The countries of Central and Eastern Europe moved from a previously centrally planned economy to a modern transition economy with strong market aspects. This paper proposes project management as an answer to this transition. Traditional Cost‐Benefit analysis does not respond to this purpose. Indeed Cost‐Benefit analysis is only interested in one specific project and not in a competition between projects. In addition all goals (objectives) have to be translated into money terms, leading sometimes to immoral consequences. On the contrary Multi‐Objective Optimization takes care of different objectives, whereas the objectives keep their own units. However different methods exist for the application of Multi‐Objective Optimization. The authors tested them after their robustness resulting in seven necessary conditions. MOORA (Multi‐Objective Optimization by Ratio analysis) and MULTIMOORA (MOORA plus Full Multiplicative Form), assisted by Ameliorated Nominal Group and Delphi Techniques, satisfy the seven conditions, although in a theoretical way. A simulation exercise illustrates the use of these methods, ideals to be strived for as much as possible.
Santrauka
Centrinės ir rytų Europos šalys perėjo iš anksčiau centralizuotai planuojamos ūkinės sistemos į šiuolaikinę pereinamąją ūkinę sistemą, kuriai būdingi ryškūs rinkos požymiai. Šiame straipsnyje siūloma projektų vadyba kaip atsakas į perėjimą. Įprastinė kainos ir naudos analizė tam tikslui yra netinkama. Be viso to, kainos ir naudos analizėje neatsižvelgiama į kiekvieną atskirai paimtą projektą bei į konkurenciją tarp tų projektų. Visi tikslai turi būti pakeisti piniginėmis vertėmis. Del to kartais kyla nepageidaujamų pasėkmių. Priešingai tam daugiatikslė optimizacija atsižvelgia į skirtingus tikslus, išsaugant tikslams būdingus mato vienetus. Yra daug įvairių daugiatikslės optimizacijos metodų. Autoriai patikrino jų stipriasias savybęs pagal septynias būtinasias sąlygas. MOORA (daugiatikslė optimizacija santykių dydžių analizės pagrindu) ir MULTIMOORA (MOORA plius pilnoji sandaugos forma), apimanti patobulintą normaliųjų grupių ir Delphi būdus, geriausiai atitinka septynias būtinąsiąs sąlygas taip pat ir teoriniu lygmeniu. Pavyzdžio modelis iliustruoja šiu metodu taikymą, idealai buvo pasiekti tiek, kiek galima.
First published online: 21 Oct 2010
Reikšminiai žodžiai: projektu vadyba, kainos ir naudos analize, daugiatiksle optimizacija, stiprybes, patobulintas grupinis ir Delphi būdai, pilnoji multiplikatyvine forma
Fuzzy logic handles vague problems in various areas. The fuzzy numbers can represent either quantitative or qualitative variables. The quantitative fuzzy variables can embody crisp numbers, aggregates of historical data or forecasts. The qualitative fuzzy variables may be applied when dealing with ordinal scales. The MULTIMOORA method (Multiplicative and Multi-Objective Ratio Analysis) was updated with fuzzy number theory. The MULTIMOORA method consists of three parts, namely Ratio System, Reference Point and Full Multiplicative Form. Accordingly, each of them was modified with triangular fuzzy number theory. The fuzzy MULTIMOORA summarizes the three approaches. The problem remains how to summarize them. It cannot be done by summation as they are composed of ranks (ordinal). Indeed summation of ranks is against any mathematical logic. Another method, the Dominance Method, is used to rank the EU Member States according to their performance in reaching the indicator goals of the Lisbon Strategy 2000–2008. This ranking will group the best performing countries in a Core Group, followed by a Second Group, the Semi-periphery Group. Group 3, the Periphery Group, will encompass the less performing states.
A new method is proposed for multi-objective opti-mization with discrete alternatives: MOORA (Multi-Objective Op-timization on the basis of Ratio Analysis). This method refers to a matrix of responses of alternatives to objectives, to which ratios are applied. A well established other method for multi-objective opti-mization is used for comparison, namely the reference point method. Later on, it is demonstrated that this is the best choice among the different competing methods. In MOORA the set of ratios has the square roots of the sum of squared responses as denominators. These ratios, as dimensionless, seem to be the best choice among different ratios. These dimensionless ratios, situated between zero and one, are added in the case of maximization or subtracted in case of min-imization. Finally, all alternatives are ranked, according to the ob-tained ratios. Eventually, to give more importance to an objective, an objective can be replaced by different sub-objectives or a coeffi-cient of importance can be specified. An example on privatization in a transition economy illustrates the application of the method. If application is situated originally in a "welfare" economy, centered on production, MOORA becomes even more significant in a "wellbeing economy", where consumer sovereignty is assumed.
The number of adult learners who participate in online learning has rapidly grown in the last two decades due to online learning's many advantages. In spite of the growth, the high dropout rate in online learning has been of concern to many higher education institutions and organizations. The purpose of this study was to determine whether persistent learners and dropouts are different in individual characteristics (i.e., age, gender, and educational level), external factors (i.e., family and organizational supports), and internal factors (i.e., satisfaction and relevance as sub-dimensions of motivation). Quantitative data were collected from 147 learners who had dropped out of or finished one of the online courses offered from a large Midwestern university. Dropouts and persistent learners showed statistical differences in perceptions of family and organizational support, and satisfaction and relevance. It was also shown that the theoretical framework, which includes family support, organizational support, satisfaction, and relevance in addition to individual characteristics, is able to predict learners' decision to drop out or persist. Organizational support and relevance were shown to be particularly predictive. The results imply that lower dropout rates can be achieved if online program developers or instructors find ways to enhance the relevance of the course. It also implies that adult learners need to be supported by their organizations in order for them to finish online courses that they register for.
Industry 4.0 represents the fourth industrial revolution in production; manufacturing and industry. Industry 4.0 connects new technologies providing flexibility in manufacturing where the conditions change rapidly. Companies need to use Industry 4.0 technologies to take their place in a competitive environment. Evaluating companies’ performance based on Industry 4.0 is a complex multi criteria problem including both quantitative and qualitative factors. In this chapter, we propose a novel fuzzy MULTIMOORA method based on interval-valued spherical fuzzy sets to evaluate companies that are using Industry 4.0 technologies. Five different alternatives are evaluated according to seven conflicting criteria by three decision makers. The results are compared with single-valued spherical fuzzy MULTIMOORA method. The results indicate that Industry 4.0 performance evaluating problem can be tackled by using the proposed methodology effectively.
The objective of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the neutrosophic set environment. Single-valued and interval neutrosophic sets are the important mechanisms for directing the decision-making queries with unknown and indeterminant data by employing a degree of “acceptance”, “indeterminacy”, and “non-acceptance” in quantitative terms. Also, to describe the behavior of the decision-maker objectively (in terms of probability) and subjectively (in terms of weights), a concept of probabilistic information plays a dominant role in the investigation. Keeping these features in mind, this paper presents several probabilistic and immediate probability-based averaging and geometric aggregation operators for the collection of the single-valued and interval neutrosophic sets. The advantage of these proposed operators is that it simultaneously combines the objective and subjective behavior of the decision-maker during the process. The various salient features of the proposed operators are studied. Later, we develop two new algorithms based on the aggregation operators to solve multiple attribute decision-making problems with single-valued and interval neutrosophic sets features. A numerical example related to the demonetization is given to demonstrate the presented approaches, and the advantages, as well as comparative analysis, are given to shows its influence over existing approaches.
In the multi-criteria decision-making (MCDM), multi-objective optimisation by ratio analysis (MOORA) plus the full multiplicative form (MULTIMOORA) are a useful method, which has the flexibility and robustness properties. The aim of this paper is to present a more robust method of MULTIMOORA to solve the MCDM evaluations with interval-valued Pythagorean fuzzy sets (IVPFSs). More specifically, considering the mutual support relationship among the input arguments, we firstly extend the power average (PA) and power geometric (PG) operators to accommodate the interval-valued Pythagorean fuzzy environment. For this, we propose four aggregation operators, including the interval-valued Pythagorean fuzzy power average (IVPFPA), the weighted interval-valued Pythagorean fuzzy power average (WIVPFPA), the interval-valued Pythagorean fuzzy power geometric (IVPFPG) and the weighted interval-valued Pythagorean fuzzy power geometric (WIVPFPG). With the aid of WIVPFPA and WIVPFPG, we further put forward a new robustness of the ranking method, i.e., the interval-valued Pythagorean fuzzy power average-based MULTIMOORA (IVPFPA-MULTIMOORA). Due to the availability and vast diversity among open-source electronic health record (EHR) systems, choosing an appropriate system is a challenge for many health-care institutions under the interval-valued Pythagorean fuzzy environment. Based on these above-mentioned research findings, we successfully utilise the IVPFPA-MULTIMOORA method to solve the selection problem of hospital open-source EHRs systems for MedLab in Ghana. Meanwhile, the effectiveness of the proposed method is verified by some comparative analyses.
The car sharing is an effective supplement to public transportation systems. However, how to select an appropriate site for building a car sharing station is a big challenge. Therefore, in this paper, a novel picture fuzzy multi-criteria decision making (MCDM) model is proposed to solve the site selection problem for car sharing stations. To this end, the definition of picture fuzzy sets is adopted to accurately portray the voting information. Then, a concept of knowledge measure is defined for PFNs and an objective method based on knowledge measure is proposed to derive the weight information of criteria. To rank the candidate sites for car sharing stations, an extended MULTIMOORA method based on novel score function and Borda rule is devised. The proposed MCDM model is applied to solve the site selection for car sharing stations in Bejing. Finally, comparative analyses are given to verify the superiority of the proposed MCDM model.
This manuscript presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can trade with only one-dimensional problems due to which some important knowledge may be lost in some situations. A modification to these, CIF sets are portrayed by complex-valued degrees of satisfaction and dissatisfaction and handle two-dimensional data concurrently in one set using additional terms, called phase terms, which usually give knowledge related with periodicity. Motivated by the features of the CIF model, we present some aggregation operators, namely, generalised CIF Bonferroni mean and generalised CIF weighted Bonferroni mean. Some features related to proposed operators are addressed. In light of the developed operators, a decision-making method is put forward and is drawn with the aid of an example. The reliability of the presented decision-making method is examined with the help of a validity test and by comparing the results of the example with several predominating studies.
Linguistic single-valued neutrosophic set ( LSVNS ) is a more reliable tool, which is designed to handle the uncertainties of the situations involving the qualitative data. In the present manuscript, we introduce some power aggregation operators ( AOs ) for the LSVNSs, whose purpose is to diminish the influence of inevitable arguments about the decision-making process. For it, first we develop some averaging power operators, namely, linguistic single-valued neutrosophic ( LSVN ) power averaging, weighted average, ordered weighted average, and hybrid averaging AOs along with their desirable properties. Further, we extend it to the geometric power AOs for LSVNSs. Based on the proposed work; an approach to solve the group decision-making problems is given along with the numerical example. Finally, a comparative study and the validity tests are present to discuss the reliability of the proposed operators.
Purpose
In this paper, we aim to present the Augmented Reality eyeglass selection problem based on Neutrosophic MULTIMOORA method which is a very new multi-objective method.
Design/methodology/approach
We evaluate five Augmented Reality goggles according to six different criteria. Criteria have different weights and determined by Analytic Hierarchy Process. We use neutrosophic MULTIMOORA method in order to evaluate Augmented Reality eyeglasses..
Findings
Five different Augmented Reality eyeglassess were evaluated and selected the best one according to six different critera ( benefit and non-benefit). According to neutrosophic MULTIMOORA method, Sony ugmented Reality eyeglass is selected the best one. Neutrosophic MULTIMOORA method uses simple computational equations and it handles multi- objective decision making problems effectively.
Originality/value
Evaluating AR goggles by using the Neutrosophic MULTIMOORA method for the first time is the originality of this paper.
With the development of modern technology, industrial robots have been applied extensively in different industries to perform high-risk jobs and produce high-quality products. However, selecting an appropriate robot for a specific manufacturing environment is a difficult task for decision makers because of the increase in complexity, production demands, and the availability of different robot types. Normally, robot selection can be regarded as a complex multicriteria decision-making problem, and decision makers often use uncertain linguistic terms to express their assessments because of time pressure, lack of data, and their limited expertise. In this article, a modified MULTIMOORA (Multiobjective Optimization by Ratio Analysis plus the Full Multiplicative Form) method based on hesitant fuzzy linguistic term sets (named HFL-MULTIMOORA) is proposed for evaluating and selecting the optimal robot for a given industrial application. This method deals with the decision makers' uncertain assessments with hesitant fuzzy linguistic variables, which can increase the flexibility of representing linguistic information. Finally, an empirical example is presented to demonstrate the proposed method, and the results indicate that the HFL-MULTIMOORA provides a useful and practical tool for solving robot selection problems within a hesitant linguistic information environment.
In this paper, a novel decision methodology of critical path determination is introduced that not only considers project time but also considers project cost, risk, quality and safety. To address uncertain project environment, interval type-2 fuzzy sets (IT2FSs) are presented in the proposed decision methodology. The ratings of each activity and the weight of each criterion are described by IT2F-numbers. To address this multi-criteria decision problem, a new version of MULTIMOORA and MOOSRA methods are extended to IT2F-uncertainty and are used to determine project’s critical paths. In addition to addressing IT2FSs, the method is enhanced by replacing the commonly applied dominance theory by a new version of multi-approaches multi-criteria decision-making technique, namely technique of precise order preference (TPOP). Finally, in order to display the applicability of the presented methodology, an existing case study from the literature to aircraft prototype batch is adopted and solved. Furthermore, a case study of construction project is solved by proposed methodology. Also, sensitivity analysis and comparative analysis are carried out, and the results are discussed. The validity of the proposed methodology is confirmed by solving two decision methods of the recent literature. Furthermore, the sensitivity analysis illustrates that the critical path of the project is approximately insensitive to weights of new MULTIMOORA method's main parts.
Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient's blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts' opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.
Failure mode and effects analysis (FMEA) is one of the most important risk assessment tools which has been extensively used in different industries and organizations. In the conventional FMEA, sometimes the difference between some failure modes cannot be distinguished. In order to evaluate various failure modes more precisely, a novel fuzzy hybrid model for FMEA is proposed in this paper. In this method, fuzzy weighted risk priority number (FWRPN) is considered instead of RPN for each failure. The weights of the three factors and the weights of failure modes are computed by extended fuzzy AHP and fuzzy MULTIMOORA methods, respectively. The proposed fuzzy MULTIMOORA method calculates the weight of each failure based on three criteria of time, cost, and profit through fuzzy linguistic terms. After calculating FWRPN for each failure, corrective actions are performed for eliminating the identified failures or decreasing the effects of them. Then, corrected fuzzy weighted risk priority number (CFWRPN) is computed for each failure. Finally, the average of FWRPNs (AFWRPNs) with the average of CFWRPNs (ACFWRPNs) are compared to evaluate the effectiveness of corrective actions by a novel ranking fuzzy numbers method. In addition, the proposed ranking fuzzy number method is also used in both previously mentioned fuzzy multi-criteria decision making (MCDM) methods. Eventually, Kerman Steel Industries Factory is considered as a case study to demonstrate the applicability and benefits of the proposed fuzzy hybrid method. A sensitivity analysis is performed to validate the obtained results. Findings show that AFWRPNs decreased by 56% compared to ACFWRPNs.
This article aims to create a theoretical evaluation model based on decision support methods for the residential house construction materials and elements selection. The research and analyses of most of the scientists are invoked on individual elements and materials of the building, which have an impact on different aspects of sustainability. Meanwhile, the integrated model covering all the key elements and materials of the single-family residential house has not been implemented. Thus, the problem of development of the general composite model of the element and material selection of single-family buildings is acute in many countries around the world.
Our study assessed the specific technical parameters related to building materials: cost, thermal bridging, and load-bearing capacity, the outer material selection according to localisation, environmental performance, durability, weight. SWARA (Step-wise Weight Assessment Ratio Analysis) approach is applied to decision making to calculate the relative importance of the criteria. A single-valued neutrosophic set governs the proposed new extension of MULTIMOORA (Multiobjective Optimisation by Ratio Analysis Plus Full Multiplicative Form) method and allows to deal explicitly with the indeterminacy of the initial information. Our proposed new theoretical composite model for selection of elements, materials and other aspects of sustainability can be practically applied in creating the decision support system for the selection of single-family house elements and materials.
The objective of this paper is to present some series of geometric-aggregated operators under Pythagorean fuzzy environment by relaxing the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted geometric, Pythagorean fuzzy Einstein ordered weighted geometric, generalized Pythagorean fuzzy Einstein weighted geometric, and generalized Pythagorean fuzzy Einstein ordered weighted geometric operators, are proposed in this paper. Some of its properties have also been investigated in details. Finally, an illustrative example for multicriteria decision-making problems of alternatives is taken to demonstrate the effectiveness of the approach.
The process of multiple criteria decision making (MCDM) is of determining the best choice among all of the probable alternatives. The problem of supplier selection on which decision maker has usually vague and imprecise knowledge is a typical example of multi criteria group decision-making problem. The conventional crisp techniques has not much effective for solving MCDM problems because of imprecise or fuzziness nature of the linguistic assessments.
The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets (PFSs). The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging (PFEWA), Pythagorean fuzzy Einstein ordered weighted averaging (PFEOWA), generalized Pythagorean fuzzy Einstein weighted averaging (GPFEWA), and generalized Pythagorean fuzzy Einstein ordered weighted averaging (GPFEOWA), are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.
As a generalization of fuzzy set, hesitant fuzzy set permits the membership degree of an element to a set being represented by several possible values and thus can be considered as a powerful tool to express uncertain information in the process of group decision making. The aim of this study is to present a multi-criteria decision making method, namely MULTIMOORA-HF, to tackle hesitant fuzzy information. Being an extension of the crisp MULTIMOORA method, the MULTIMOORA-HF is designed to facilitate group decision making with uncertain information. The proposed methods consists of the three parts-the Ratio System, the Reference Point, and the Full Multiplicative Form. The proposed method thus provides the means for multi-criteria decision making related to uncertain and complex assessments. Utilization of aggregation operators also enables to reduce subjectivity and bias in the group multi-criteria decision making. The numerical simulation exhibits the possibilities for application of the proposed method.
The paper presents a multi-criteria decision making method to tackle intuitionistic fuzzy numbers, namely MULTIMOORA-IFN. Being an extension of the crisp MULTIMOORA method, the MULTIMOORA-IFN is designed to facilitate group decision making with uncertain information. The proposed methods consists of the three parts—the Ratio System, the Reference Point, and the Full Multiplicative Form—specific with different aggregation techniques. Furthermore, the robustness of the decision making process can be improved by employing ordered aggregation operators, for instance an intuitionistic fuzzy power ordered weighted average operator or an intuitionistic fuzzy power ordered weighted geometric operator. A numerical simulation exhibits the possibilities for application of the proposed method.
Student selection is a multi-criteria decision making problem which includes both tangible and intangible factors. In these problems if educational institutions have budget or other different constraints two problems will exist: which students are the best and how students are assigned to the predefined programs? In this study, an integrated approach of fuzzy MULTIMOORA and multi-choice conic goal programming is proposed to consider criteria in choosing the best students and define the optimum assignments among the predefined programs to maximize both of the total preference value and the total ranking value. The ranks of the students are determined by using fuzzy MULTIMOORA. The ranks of candidates are set as the parameters of the first objective function. The placement preferences of the students according to the predefined programs are considered in the second objective function. The candidates are assigned to their placement preferences both by using multi-choice conic goal programming among partner universities according to the objectives and by considering the budget and quota.
We introduce a new class of non-standard fuzzy subsets called Pythagorean fuzzy subsets and the related idea of Pythagorean membership grades. We focus on the negation operation and its relationship to the Pythagorean theorem. We compare Pythagorean fuzzy subsets with intuitionistic fuzzy subsets. We look at the basic set operations for the Pythagorean fuzzy subsets.
Personnel selection process is aimed at choosing the best candidate to fill the defined vacancy in a company. It determines the input quality of personnel and thus plays an important role in human resource management. Given the uncertain, ambiguous, and vague nature of personnel selection process, it requires the application of multi-criteria decision making (MCDM) methods for robust recruitment. This paper hence is aimed at extending the fuzzy MULTIMOORA for linguistic reasoning under group decision making. The fuzzy MULTIMOORA was further modified in this study. The fuzzy MULTIMOORA for group decision making (MULTIMOORA–FG) enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform more robust personnel selection procedures. A personnel selection problem illustrated the group decision-making procedure according to MULTIMOORA–FG: the enterprise has formed an executive committee consisting of four decision-makers to choose the best candidate from another four participants to fill the vacancy. The committee has decided to consider eight qualitative attributes expressed in linguistic variables. The numerical example exhibited possibilities for improvement of human resources management as well as any other business decision area by applying MULTIMOORA–FG.
Strategic planning of e-learning implementation includes decision making about the most suitable form of implementing e-learning
on different levels in an institution. Decision making about e-learning implementation has been covered as consisting of four
phases: (1) intelligence, (2) design, (3) choice and (4) implementation. During the Intelligence phase we have precisely identified
our central decision problem and have conducted situation analysis. In the Design phase we have developed alternatives and
established criteria and subcriteria. The questionnaire about the importance of the advantages and goals of e-learning implementation
and about criteria and subcriteria significant for decision making was created. Essential for the survey was use of Croatian
e-learning experts that are familiar with higher education (HE) environment. Further, we connected these findings with the
results of the factor analysis which was performed on the survey. The results of the factor analysis have served as input
in the multicriteria decision model (AHP) that we have developed in the Choice phase. In the implementation phase we have
solved the problem of prioritisation of e-learning options with the help of multi-criteria modelling in the process of group
decision making. In this article, firstly we will present and analyze the results of the survey. Secondly, the outputs of
factor analysis will be stated and compared with the model used in the questionnaire. Finally, the structure of AHP model
will be given and the results of the quantitative evaluation of the model will be presented.
A sound decision methodology for evaluating and selecting e-learning products should consider multiple and conflicting criteria and the interactions among them. In this paper, a decision framework which employs quality function deployment (QFD), fuzzy linear regression and optimization is presented for e-learning product selection. First, a methodology for determining the target values for e-learning product characteristics that maximize overall customer satisfaction is presented. The QFD framework is employed to allocate resources and to coordinate skills and functions based on customer needs. Differing from earlier QFD applications, the proposed methodology employs fuzzy regression to determine the parameters of functional relationships between customer needs and e-learning product characteristics, and among e-learning product characteristics themselves. Finally, the e-learning product alternatives are evaluated and ranked with respect to deviations from the target product characteristic values. The potential use of the proposed decision framework is illustrated through an application on e-learning products provided by the universities in Turkey.
As online and blended learning has become common place educational strategy in higher education, educators need to reconceptualise fundamental issues of teaching, learning and assessment in non traditional spaces. These issues include concepts such as validity and reliability of assessment in online environments in relation to serving the intended purposes, as well as understanding how formative assessment functions within online and blended learning. This article provides a systematic qualitative review of the research literature on online formative assessment in higher education. As an integrative narrative review, the method applied in this review entailed systematic searching, reviewing, and writing this review of the literature to bring together key themes and findings of research in this field. The authors applied qualitative thematic criteria in selecting and reviewing the available literature from which they focused on identifying and analyzing the core themes that are central to the concept of formative assessment with a key focus on application of formative assessment within blended and online contexts. Various techniques were identified for formative assessment by the individual, peers and the teacher, many of which were linked with online tools such as self-test quiz tools, discussion forums and e-portfolios. The benefits identified include improvement of learner engagement and centrality in the process as key actors, including the development of a learning community. The key findings are that effective online formative assessment can foster a learner and assessment centered focus through formative feedback and enhanced learner engagement with valuable learning experiences. Ongoing authentic assessment activities and interactive formative feedback were identified as important characteristics that can address threats to validity and reliability within the context of online formative assessment.