Multiple Criteria Group Decision Making Problems Research Articles

A Comparative Study on the Generalized Spherical Fuzzy Einstein Aggregation Operators

Generalized spherical fuzzy set theory is a powerful and useful tool that is capable to process uncertainty and vagueness. In this study, we investigate some induced aggregation operators under the generalized spherical fuzzy environment with the help of Einstein norms operations to merge the generalized spherical fuzzy information into a single one in the decision-making process. After we observe some properties of the presented aggregation operators, we establish an algorithm to use in the solution of the multiple criteria group decision-making problems by using these aggregation operators and also we give an illustrative example. Then, we compare the results under all defined generalized spherical fuzzy Einstein aggregation operators used within the decision-making process.

A PCA-based fuzzy tensor evaluation model for multiple-criteria group decision making

Multiple-criteria group decision-making (MCGDM) problems mainly consist of multiple factors and multiple Decision Makers (DMs) or Users, for which dimension extension is necessary when considering all the entries of DMs together. Tensor, a generalized form of a matrix, displays a multi-way array item, which is the most suitable and practical way to represent high-dimensional data without losing any information. In this paper, we first reduce the dimension through Principal Component Analysis (PCA), which helps consider the most-informative criteria. Then, we reintroduced the tensor as a fuzzy-form tensor for the MCGDM problem because of user information uncertainty. We choose Interval-valued Neutrosophic Fuzzy numbers (IVNFNs) as the basis for the tensor form because of their ability to distinguish between truth, indeterminacy, and falsity in the data. Lastly, a Generalized Interval-valued Neutrosophic Fuzzy Weighted Geometric (GIVNFWG) operator is defined. Moreover, a generalized framework for fuzzy-form tensors for high-dimensional MCGDM problems is proposed. The feasibility and efficiency of this proposed process is illustrated for a real-world MCGDM problem of ranking the most efficient Third Party Reverse Logistics Partners (3PRLPs), i.e., recycled fiber-based paper mills for the packaging industry. The obtained results are according to the experts and are validated using sensitivity analysis. This analysis facilitates in assessing the impact on the overall ranking performance of 3PRLPs by considering various combinations of environment and technological sub-criteria.

A Novel Spherical Fuzzy Bi-Objective Linear Assignment Method and Its Application to Insurance Options Selection

Spherical fuzzy sets are the latest extension of the ordinary fuzzy sets. The main characteristic of the spherical fuzzy sets is satisfying the condition that the squared sum of the membership, nonmembership, and hesitancy degrees must be at least zero and at most one. In this research, by extending the classical linear assignment method to bi-objective linear assignment and integrating it with cosine similarity measure, we presented a novel beneficial method for solving multiple criteria group decision-making problems in the spherical fuzzy environment. A new concept for weighting the criteria, which is composed of positive and negative impacts (weights), is introduced. The proposed bi-objective model tries to maximize positive impacts and minimize the negative impacts simultaneously. In order to solve the bi-objective linear assignment model, [Formula: see text]-constraint method is applied. Therefore, a trade-off solution is formed between maximizing positive impacts and minimizing negative impacts. The applicability and validity of the proposed method are shown through an insurance options selection problem. To test the reliability and validity of the proposed method, comparative and sensitivity analysis are performed.

Probabilistic uncertain linguistic TODIM method based on the generalized Choquet integral and its application

PurposeThe purpose of this paper is to develop a probabilistic uncertain linguistic (PUL) TODIM method based on the generalized Choquet integral, with respect to the interdependencies between criteria, for the selection of the best alternate in the context of multiple criteria group decision-making (MCGDM).Design/methodology/approachOwing to decision makers (DMs) do not always show completely rational and may have the preference of bounded rational behavior, this may affect the result of the MCGDM. At the same time, criteria interaction is a focused issue in MCGDM. Hence, a novel TODIM method based on the generalized Choquet integral selects the best alternate using PUL evaluation, where the generalized Choquet integral is used to calculate the weight of criterion. The generalized PUL distance measure between two probabilistic uncertain linguistic elements (PULEs) is calculated and the perceived dominance degree matrices for each alternate relative to other alternates are obtained. Furthermore, the comprehensive perceived dominance degree of each alternate can be calculated to get the ranking.FindingsPotential application of the PUL-TODIM method is demonstrated through an evaluation example with sensitivity and comparative analysis.Originality/valueAs per author's concern, there are no TODIM methods with probabilistic uncertain linguistic sets (PULTSs) to solve MCGDM problems under uncertainty. Compared with the result of existing methods, the final judgment value of alternates using the extended TODIM methodology is highly corroborated, which proves its potential in solving MCGDM problems under qualitative and quantitative environments.

The multicriteria group decision making FlowSort method under uncertainty

Crisp values are insufficient to model real-life situations and imprecise ideas are frequently represented in multicriteria decision aid analysis. In fact, it is difficult to treat the evaluation criteria precisely and to fix exact preferences rating. The triangular intuitionistic fuzzy numbers succeeded to treat this kind of ambiguity in a great deal of research than other forms of fuzzy representation functions. The field of sorting issues is an active research topic in the multiple criteria decision aid (MCDA). This study extended one of the sorting methods, FLOWSORT, for solving multiple criteria group decision-making problems. This extension described the preferences rating of alternatives as linguistic terms which can be easily expressed in triangular intuitionistic fuzzy numbers. To validate our extension, an illustrative example as well as an empirical comparison with other multi-criteria decision making methods is presented. Keywords: multicriteria group decision making, sorting problematic, intuitionistic fuzzy set, FlowSort method

WASPAS-based decision making methodology with unknown weight information under uncertain evaluations

The uncertain probabilistic linguistic term set (UPLTS) one of the modern development in fuzzy set theory, can express not only the decision makers (DMs) linguistic assessment information but also the uncertain probability/weight/importance degree of each linguistic assessment value, so it is an efficient tool for addressing the ignorance problems. The current study mainly focuses on developing a more effective way to cope with multiple criteria group decision making (MCGDM) problems in which the assessment information are in the form of UPLTSs, and the weight information is also entirely unknown. Firstly, some weaknesses of the existing operational laws and score function of UPLTSs are pointed out through some critical examples and then redefined them to overcome existing flaws in order to acquire more accurate results in practical decision making problems. Also, we establish various properties of the revised operational laws along with proofs. To design a novel comparison method, the concept of deviation degree is introduced in order to accommodate the situation in which two different UPLTSs have the same score values. After that, based on the proposed operational laws, several existing aggregation operators are modified, and a novel aggregation operator, namely uncertain probabilistic linguistic simple weighted geometry (UPLSWG) operator is designed. Meanwhile, some interesting properties of these proposed operators are carefully analysed. Furthermore, an entropy technique under uncertain probabilistic linguistic information is structured for computing the completely unknown weights of criteria. Following this, a new extension of weighted aggregated sum product assessment (WASPAS) method called uncertain probabilistic linguistic-WASPAS (UPL-WASPAS) methodology based on the proposed aggregation operators is studied under the UPLTS context for ranking objects in MCGDM problems. To show the applicability and potentiality of the developed method, an example of supplier selection is addressed, and a detailed performance comparison analysis is conducted. Furthermore, sensitivity analysis is also made to determine the impact of the parameter on the ranking of alternatives.

An Improved PL-VIKOR Model for Risk Evaluation of Technological Innovation Projects with Probabilistic Linguistic Term Sets

Risk evaluation is a primary but important task for technological innovation projects and this task is a multiple criteria group decision-making (MCGDM) process with probabilistic uncertainty and fuzzy uncertainty. Compromise programming decision-making methods with probabilistic linguistic term sets (PLTSs) are more appropriate for risk evaluation of technological innovation projects. This paper proposes a new approach named improved probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (PL-VIKOR) method with probabilistic linguistic term sets for risk evaluation of technological innovation projects. Firstly, by fully considering both the relationship between each alternative and the positive ideal solution and the relationship between each alternative and negative ideal solution, the improved PL-VIKOR method for dealing with MCGDM problems is developed to make up the deficiency of the traditional PL-VIKOR method. Then, the improved PL-VIKOR method is applied to solve a practical MCGDM problem with probabilistic linguistic term sets involving the risk evaluation of technologically innovative projects for venture capital. Finally, we make some comparative analyses between the improved PL-VIKOR method and some existing methods to analyze the advantages and disadvantages of the proposed method. The results reflect that the improved PL-VIKOR method is more reasonable when calculating the distance measure between two PLTSs, and it can make the risk evaluation of technological innovation project MCGDM with PLTSs more objective.

Extensions of ELECTRE-I and TOPSIS methods for group decision-making under complex Pythagorean fuzzy environment

Multi-criteria group decision-making is a process in which decision makers assess the performance of alternatives on the basis of conflicting criteria to opt the most worthy alternative as solution. TOPSIS and ELECTRE are effective and commonly used methods to solve multiple criteria decision-making problems. The aim of this study is to propose two new models, namely, complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method and complex Pythagorean fuzzy ELECTRE I (CPF-ELECTRE I) method, to tackle multiple criteria group decision-making problems comprising complex Pythagorean fuzzy data. In these methods, we compare complex Pythagorean fuzzy numbers on the basis of their score functions. We use revised closeness index for the ranking of alternatives in CPF-TOPSIS method. {In complex Pythagorean fuzzy concordance and discordance sets, we compare the alternatives on being superior and inferior to other alternatives on the basis of score degree, accuracy degree and indeterminacy. In CPF-ELECTRE I method, we use outranking decision graph to obtain the best alternative.} We illustrate the structure of both methods with the help of flow charts. To verify the accuracy of {proposed methods}, we present an explanatory example for selection of best interior designer for a hotel renovation. {We authenticate the proposed techniques by providing a brief comparative analysis of these methods with existing methods}.

An Extended MABAC Method Based on Triangular Fuzzy Neutrosophic Numbers for Multiple-Criteria Group Decision Making Problems

In this manuscript, we extend the traditional multi-attributive border approximation area comparison (MABAC) method for the multiple-criteria group decision-making (MCGDM) with triangular fuzzy neutrosophic numbers (TFNNs) to propose the TFNNs-MABAC method. In the proposed method, we utilize the TFNNs to express the values of criteria for each alternative in MCGDM problems. First, we briefly acquaint the basic concept of TFNNs and describe its corresponding some operation laws, the functions of score and accuracy, and the normalized hamming distance. We then review two aggregation operators of TFNNs. Afterward, we combine the traditional MABAC method with the triangular fuzzy neutrosophic evaluation and provide a sequence of calculation procedures of the TFNNs-MABAC method. After comparing it with some TFNNs aggregation operators and another method, the results showed that our extended MABAC method can not only effectively handle the conflicting attributes, but also practically deal with incomplete and indeterminate information in the MCGDM problem. Therefore, the extended MABAC method is more effective, conformable, and reasonable. Finally, an investment selection problem is demonstrated as a practice to verify the reasonability of our MABAC method.

The likelihood-based optimization ordering model for multiple criteria group decision making with Pythagorean fuzzy uncertainty

The purpose of this paper is to propose a useful likelihood measure for determining scalar function order relations and developing a novel likelihood-based optimization ordering model for solving multiple criteria group decision making (MCGDM) problems based on Pythagorean fuzzy (PF) sets. This paper scrutinizes PF order relations based on scalar functions to compare sophisticated uncertain information and establish a precedence order. By way of scalar function order relations, this paper utilizes scalar functions that are associated with Pythagorean membership grades and admissible upper approximations to present a novel likelihood measure in PF contexts. With the aid of useful concepts, such as levels of agreement and disagreement and comprehensive performance values, this paper originates a PF likelihood-based optimization ordering model to acquire the optimal group consensus solution for addressing MCGDM problems. Practical applications and several comparative studies are performed to reveal the practicality and strong points of the proposed methodology in tackling real-world MCGDM issues within uncertain environments of PF sets. This paper finds that the new scalar function-based likelihood measure is more flexible and beneficial than the current probability distribution approach. Furthermore, an easy-to-use algorithmic procedure can realize the proposed methodology to efficaciously process sophisticated PF information and improve the understandability of a decision model via a likelihood comparison approach. The originality and main contributions of this work are fourfold: (1) A PF likelihood measure is introduced as a basis for scalar function order relations; (2) the PF likelihood-based optimization ordering model is established for consensus ranking; (3) a predominant procedure is constructed for addressing PF information; and (4) the likelihood-based decision models are enriched under complex uncertainty.

A Novel Group Decision-Making Approach for Hesitant Fuzzy Linguistic Term Sets and Its Application to VIKOR

This paper develops a novel group decision-making (GDM) approach for solving multiple-criteria group decision-making (MCGDM) problems with uncertainty. The hesitant fuzzy linguistic term sets (HFLTSs) are applied to elicit the decision makers’ linguistic preferences due to their distinguished efficiency and flexibility in representing uncertainty. However, the existing context-free grammar for linguistic description cannot allow generating the linguistic expressions completely free to limit the richness of HFLTSs, and the related methods for dealing with HFLTSs also have limitations in aggregating HFLTSs with different lengths and types. Therefore, this paper proposes extended context-free grammar and a novel GDM approach for HFLTSs, considering the advantages of the rough set theory and OWA operators. The rough set theory can manage the uncertainty existing in the fuzzy representation and deal with HFLTSs represented by the 2-tuple fuzzy linguistic model to get rough number sets. The OWA operator can aggregate these sets with different numbers of elements into an interval simply and objectively. Then, an extended VIKOR method based on the proposed GDM approach for HFLTSs is presented to solve the MCGDM problems. Finally, two examples are given to illustrate the applicability and validity of the developed GDM approach and the hesitant VIKOR method through sensitivity and comparison analysis with other existing approaches.

A Choquet integral-based hesitant fuzzy gained and lost dominance score method for multi-criteria group decision making considering the risk preferences of experts: Case study of higher business education evaluation

With the rapid development of higher business education, higher business education evaluation has attracted considerable attention of researchers and practitioners. The higher business education evaluation is an essential part of the development of a business school, which has a direct impact on its resource distribution. The higher business education evaluation can be considered as a multiple criteria group decision making (MCGDM) problem that involves a group of experts. Due to the complexity of the decision-making problem, decision criteria are not fully independent to each other, and the assumption of complete rationality of experts is usually invalid in many situations. In this paper, we propose a Choquet integral-based hesitant fuzzy gained and lost dominance score method to address the two important issues regarding the interactions among criteria and the behavior preference characteristics of experts in MCGDM problems. Firstly, a comprehensive distance measure of hesitant fuzzy sets is introduced by considering the relative importance of two separations. Then, a Choquet integral-based hesitant fuzzy gained and lost dominance score method based on the prospect theory is proposed to address the MCGDM problems in which experts make decision with the risk preference psychology. Finally, an illustrative example of higher business education evaluation is provided to demonstrate the applicability of the proposed method, and the sensitivity and comparative analysis are also completed to verify the validity of the proposed method.

Multiple criteria group decision making based on group satisfaction

To generate solutions to multiple criteria group decision-making (MCGDM) problems that are satisfactory to the decision makers, this paper proposes a new method. To examine whether a group solution is satisfactory to the decision makers, group satisfaction is constructed from alternative assessment and ranking differences between the decision makers and the group. The difference between a decision maker's assessment and a group's assessment is designed based on differences in assessment grades, whose normalization is theoretically proven to construct alternative assessment differences. Inspired by Spearman's rank correlation coefficient, the expected utilities of decision makers’ and the group's assessments are used to construct alternative ranking differences. An abstract two-variable function with specific properties is designed to relate alternative assessment difference to alternative ranking difference to form group satisfaction. From the constructed group satisfaction, the process of generating group-satisfactory solutions to MCGDM problems is presented. The problem of selecting engineering project management software is analyzed by using the proposed method to demonstrate its applicability. To highlight the importance of group satisfaction in MCGDM, relationships and differences between group satisfaction and group consensus are analyzed through the problem and simulation experiments.

Spherical Fuzzy Linear Assignment Method for Multiple Criteria Group Decision-Making Problems

Spherical fuzzy sets theory is useful and advantageous for handling uncertainty and imprecision in multiple attribute decision-making problems by considering membership, non-membership, and indeterminacy degrees. In this paper, by extending the classical linear assignment method, we propose a novel method called the spherical fuzzy linear assignment method (SF-LAM) to solve multiple criteria group decision-making problems in the spherical fuzzy environment. A ranking procedure consisting of aggregation functions, score functions, accuracy functions, weighted rank frequency, and a binary mathematical model are presented to determine the criterion-wise preferences and various alternatives’ priority order. The proposed method’s applicability and validity are shown through the selection problem among wind power farm locations. The proposed method helps managers to find the best location to construct the wind power plant based on the determined criteria. Finally, a comparative analysis is performed between the proposed spherical fuzzy linear assignment (SF-LAM) model and the spherical fuzzy analytic hierarchy process (SF-AHP) and spherical fuzzy WASPAS methods.

A multi-criteria decision-making method based on triangular interval-valued fuzzy numbers and the VIKOR method

In many cases, complex problems cannot be accurately described by precise numerical values. Fuzzy theory provides a suitable tool for solving these problems. However, if decision makers cannot reach an agreement on the method for defining linguistic variables based on fuzzy sets, TIVFNs (triangular interval-valued fuzzy numbers) can provide more accurate modeling. Therefore, solving fuzzy MCGDM (multiple criteria group decision-making) problem with an unknown expert weight and criterion weight in TIVFNs has become an important research direction. In this paper, TIVF-VIKOR (triangular interval-valued fuzzy VIKOR) method, which is suitable for the environment of TIVFNs, is proposed to solve the problem of fuzzy MCGDM. To achieve this goal, the TIVF-VIKOR method is innovatively adopted similarity and coefficient of variation are combined to calculate expert weight, and deviation maximization method based on divergence matrix is used to calculate criterion weight. VIKOR method is used to find the compromise solutions, which are converted into the form of binary connection number, and the optimal compromise solution is obtained after ranking. The proposed method is applied to the problem of machine fault detection, and the validity and feasibility of the method are illustrated. Compared with the TOPSIS∖ELECTRE method, the ranking results of the three methods are equivalent, and the fluctuation of the TIVF-VIKOR method is more distinct.

A Method Based on Bivariate Almost Stochastic Dominance for Multiple Criteria Group Decision Making With Probabilistic Dual Hesitant Fuzzy Information

Probabilistic dual hesitant fuzzy sets (PDHFSs) are sound information granules to describe decision maker's aleatory and epistemic uncertainty in multiple criteria group decision making (MCGDM) process. In this paper, a bivariate almost stochastic dominance-based PROMETHEE-II method is presented to solve probabilistic dual hesitant fuzzy MCGDM problems which consider correlation averse behavior of decision makers. First, probabilistic dual hesitant fuzzy power Bonferroni mean (PDHFPBM) operator and probabilistic dual hesitant fuzzy power geometric Bonferroni mean (PDHFPGBM) operator are proposed to acquire collective preference information of decision makers. Second, based on the defined bivariate almost stochastic dominance (BASD) and BASD degree, qualitative and quantitative relationships between two probabilistic dual hesitant fuzzy elements (PDHFEs) with corresponding to all criteria are obtained. Third, distance-based correlation coefficient method for computing combined weight with respect to all criteria is proposed. Finally, a BASD-based PROMETHEE-II method is developed to determine the ranking results. Three illustrative examples followed by comparative analysis are included to show the practicality and effectiveness of the proposed method.

A Novel Pythagorean Fuzzy LINMAP-Based Compromising Approach for Multiple Criteria Group Decision-Making with Preference Over Alternatives

This paper presents a new compromising approach to multiple criteria group decision-making (MCGDM) for the treatment of uncertainty which is based on Pythagorean fuzzy (PF) sets. The present work intends to propose a novel linear programming technique for multidimensional analysis of preference (LINMAP) by way of some useful concepts related to PF dominance relations, individual consistency and inconsistency levels, and individual fit measurements. The concept of PF scalar function-based dominance measures is defined to conduct intracriterion comparisons concerning uncertain evaluation information based on Pythagorean fuzziness; moreover, several valuable properties are also investigated to demonstrate its effectiveness. For the assessment of overall dominance of alternatives, this paper provides a synthetic index, named a comprehensive dominance measure, which is the aggregation of the weighted dominance measures by combining unknown weight information and PF dominance measures of various criteria. For each decision-maker, this paper employs the proposed measures to evaluate the individual levels of rank consistency and rank inconsistency regarding the obtained overall dominance relations and the decision-maker’s preference comparisons over paired alternatives. In the framework of individual fit measurements, this paper constructs bi-objective mathematical programming models and then provides their corresponding parametric linear programming models for generating the best compromise alternative. Realistic applications with some comparative analyses concerning railway project investment are implemented to demonstrate the appropriateness and usefulness of the proposed methodology in addressing actual MCGDM problems.

An integrated approach to green supplier selection based on the interval type-2 fuzzy best-worst and extended VIKOR methods

Green supply chain management, which considers both the environment and supply chain management, is becoming a hot topic in modern operations management. In a manufacturing enterprise, it is crucial for supply chain managers to select an appropriate supplier for their long-term development prospects to and to pursue the business strategy and remain in a competitive position. Green supplier selection (GSS) can be viewed as a multiple-criteria group decision-making (MCGDM) problem that involves many unmeasurable and conflicting criteria. Considering the advantage of interval type-2 fuzzy sets (IT2FSs) in modeling such complexity and uncertainty, this study provides an integrated methodology to address MCGDM problems based on the best-worst method (BWM) and the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique in an interval type-2 fuzzy environment. First, we extend a new decision-making method called the BWM to IT2FSs. Unlike the BWM and fuzzy BWM, our IT2FSs stem from a questionnaire survey and related interval approaches. Second, we develop an integrated model based on interval type-2 fuzzy BWM and VIKOR to solve MCGDM problems. Finally, we present a GSS example to illustrate on the performance of our approach. We also provide sensitivity and comparative analyses and a discussion of the effectiveness and advantages of the proposed method.

Multiple criteria group decision making method based on extended hesitant fuzzy sets with unknown weight information

In this paper, we initially re-define the existing definition of extended hesitant fuzzy set (EHFS) using the Cartesian product of hesitant fuzzy sets (HFSs). This is while, the EHFS concept should be defined in accordance with the number of decision makers’, and not the number of HFSs. Then we show the superiority of the proposed EHFS to the existing HFS concept by taking multiple criteria group decision making (MCGDM) problems into account in which two nonlinear optimization models are used to evaluate the weights of the decision makers and the weights of the criteria, respectively. As will be discussed in more details, the first optimization model minimizes the divergence degree of individual form of extended hesitant fuzzy decision (IEHFD) matrices, is carried out in Step 2 of the proposed algorithm for solving the MCGDM problem and the second one minimizes the divergence degree between each IEHFD matrix and the collective form of extended hesitant fuzzy decision (CEHFD) matrix, is carried out in Step 3 of the proposed algorithm for solving the MCGDM problem. Finally, we will illustrate the applicability of the proposed method to the other existing ones by dealing with a MCGDM problem under both the hesitant and the extended hesitant fuzzy environments. In addition to that, we will show that the proposed procedure leads to the more desirable result of deciding in comparison with the other existing methods, especially when we are going to generate the criteria weights.

Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness

This paper aims to utilize the core structure of linear programming technique for multidimensional analysis of preference (LINMAP) to propose a parametric LINMAP methodology for addressing multiple criteria group decision-making problems based on Pythagorean fuzzy sets. To compare Pythagorean membership grades, this paper presents a Hamming distance-based approach for identifying closeness-based order relations based on Pythagorean fuzzy closeness indices. The concept of comprehensive closeness measures is introduced to measure individual order consistency and inconsistency between subjective preference relations and objective order relations. In the spirit of LINMAP, this paper determines individual goodness of fit and poorness of fit and further constructs a novel parametric LINMAP model. The applicability of the developed approach is explored by a practical application of railway project investment. Some comparative analyses are conducted to demonstrate the usefulness and advantages of the proposed methodology.