Multi-criteria Group Decision-making Problems Research Articles

Group decision-making with hesitant fuzzy linguistic preference relations in view of worst and average indexes

To address the situation where Multi-criteria group decision-making (MCGDM) problems with hesitant fuzzy linguistic preference relations (HFLPRs), this study introduces a group decision-making (GDM) method in view of the worst additive consistency index (WACI) and average additive consistency index (AACI) simultaneously. First, several optimization models are constructed for deriving the WACI and AACI. The main characteristic of the constructed optimization models is that it takes into accounted the personalized individual semantics (PISs). And then the concept of acceptable additive consistent HFLPRs is developed based on the proposed WACI and AACI. Second, several optimization models are constructed for improving the consistency of HFLPRs. Two predefined thresholds for the WACI and AACI are considered in the proposed optimization models. It requires the consistency levels of all the linguistic preference relations (LPRs) associated with HFLPR meet the threshold of WACI, and the average consistency level of all LPRs reaches the threshold of AACI. Third, an algorithm is designed for deriving priority weights from acceptable consistent HFLPRs. Finally, the presented models are validated using a numerical example and extensive comparative analyses.

Similarity Measures of Probabilistic Interval Preference Ordering Sets and Their Applications in Decision-Making

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.

New covering techniques and applications utilizing multigranulation fuzzy rough sets

In order to conduct an in-depth study of Zhan’s methodology pertaining to the covering of multigranulation fuzzy rough sets (CMG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {C}_{{MG}}$$\\end{document}FRSs), we build two families: the family of fuzzy β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-minimum descriptions and the family of β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}-maximum descriptions. Subsequently, utilizing these notions, we proceed to develop two variations of covering via optimistic (pessimistic) multigranuation rough set samples (CO(P)MG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CO(P)}_{{MG}}$$\\end{document}FRS). The axiomatic properties are examined. In this study, we examine four models of covering using variable precision multigranulation fuzzy rough sets (CVPMG\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {CVP}_{{MG}}$$\\end{document}FRSs). We proceed with analyzing the features of these models. Interconnections between these planned plans are also elucidated. This study explores algorithms that aim to identify innovative strategies for addressing multiattribute group decision-making problems (MAGDM) and multicriteria group decision-making problems (MCGDM). The test examples have been elucidated to provide an inclusive grasp of the efficacy of the offered samples. Ultimately, the distinctions between our methodologies and the preexisting research have been demonstrated.

A group stability-based consensus model for multi-criteria group decision-making problems with linguistic distribution assessments

In multi-criteria group decision-making (MCGDM) problems with linguistic distribution assessments (LDAs), this study proposes a group stability-based consensus model to facilitate the generation of solutions that satisfy predefined group stability and group consensus requirements. The group stability and group consensus measures are constructed at the criteria, alternative, expert, and global levels. In terms of different degrees of group stability and group consensus in MCGDM problems, it can be categorized into four situations by comparing with predefined thresholds, which are: 1) group stability measure is satisfied, and group consensus measure is satisfied; 2) group stability measure is not satisfied, and group consensus measure is satisfied; 3) group stability measure is satisfied, and group consensus measure is not satisfied; 4) group stability measure is not satisfied, and group consensus measure is not satisfied. To accelerate the group stability-based group consensus reaching process, optimization problems with group stability and group consensus requirements are constructed to obtain suggested intervals and recommended intervals for LDAs. This contributes to the feedback mechanisms corresponding to the four different situations. The proposed method is applied to an ultrasonic medical imaging workstation selection problem to demonstrate its effectiveness. The superiority of the proposed method is validated through comparative experiments.

Double-layer multi-criteria group decision-making approach using neutralized possibility degree-based decision matrix with fuzzy information

Multi-criteria group decision-making (MCGDM) problems are fundamentally characterized by uncertainty and ambiguity. The quantification of such data is vital for determining the most optimal course of action. In this paper, a double-layer possibility degree-based interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) Vlsekriterijumska Optimizacija i Kompromisno Resenje (VIKOR) approach is presented. First, the possibility degrees of IVq-ROFSs are calculated and processed to establish a new neutralized decision matrix. Second, the components of the new decision matrix are taken into account for obtaining a new pair of positive and negative ideal solutions. The utility and regret measures in the VIKOR approach are ultimately determined by combining criteria weights and cumulative possibility degrees to rank the alternatives. The results of the study show that the proposed approach contributes to acquiring accurate alternative rankings in situations where traditional approaches have had difficulty generating ranks. Also, by eliminating the early normalization stage, which has a direct impact on the final ranking, the proposed approach concludes a unique ranking for each decision-making problem. Several comparative and sensitivity analysis are also conducted to exhibit robustness and applicability of the proposed approach in real world.

A fuzzy computing approach to aggregate expert opinions using parabolic and exparabolic approximation procedures for solving multi-criteria group decision-making problems

AbstractTriangular fuzzy numbers (TFNs) are widely used for selection problems to determine expert opinions using linguistic expressions. Some aggregation procedures are developed to determine expert opinions more accurately. However, there is a need for a simple and more useful procedure to solve the selection problems more suitably. For this purpose, our study offers a triangular, exparabolic, and parabolic area calculation-based approximation approach for TFNs to aggregate the possible hedges (very and more or less) for TFNs. Hence, this aggregation procedure provides a tuning opportunity for classical TFN expressions to capture possible tuning processes to reflect the hesitancies of experts. The technique for order preferences by similarity to ideal solution (TOPSIS) method is applied in the two studies from extant literature, and suitable alternatives are determined as a result of the ranking process. Finally, a comparative analysis is presented to illustrate the efficiency of the proposed procedure. The conventional TOPSIS model’s ranking scores are very close for exemplified examples (i.e., 0.5308, 0.4510, 0.4550 and 0.5304, 0.4626, 0.4940), but the proposed model’s result has fluctuated for the same examples (i.e., 0.346, 0,669, 0,567 and 0.208, 0.991, 0.148). So, the main advantage of the proposed aggregation procedure is the alternative ranking scores separation capability analyzed with their linguistic diversification.

Threshold-Based Value-Driven Method to Support Consensus Reaching in Multicriteria Group Sorting Problems: A Minimum Adjustment Perspective

In multicriteria group decision-making (MCGDM) problems, there exist the situations that alternatives need to be assigned to several predefined ordered categories rather than be ranked from the most preferred to the least preferred, which is called multicriteria group sorting problems. To address multicriteria group sorting problems, it is necessary to implement a consensus reaching process to fully consider the opinion of each decision maker and reduce the conflict among them. To do so, this article proposes a consensus reaching model for multicriteria group sorting problems based on the threshold-based value-driven sorting method from the perspective of minimum adjustment. Specifically, we first define the consensus measure to calculate the agreement degree among decision makers by considering the ordinal information and cardinal information at the same time. On this basis, we construct a minimum adjustment optimization model in terms of the threshold-based value-driven sorting method to assist decision makers in modifying their decision matrices and further promote consensus. Followed by this, an optimization model that aims to minimize the distance between all decision makers and the group with respect to alternatives’ comprehensive values and sorting results is developed to determine the group sorting result for alternatives. Moreover, a numerical application of urban park management, some sensitivity analysis, and simulation experiments are provided to justify the proposed method. Experimental results reveal that the proposed method is effective in promoting consensus.

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

A Multi-Criteria Group Decision-Making Approach For Robot Selection Using Interval-Valued Intuitionistic Fuzzy Information And Aczel-Alsina Bonferroni Means

The process of identifying the most appropriate robot for a particular industrial task has grown challenging and more difficult in the fast-paced environment. It is merely driven by the complex evolution and continuous integration of modern characteristics and advanced features by various suppliers. Industrial robots are now widely available in the marketplace, each possessing a distinctive collection of skills, attributes, and requirements. However, the selection of optimal robots is heavily influenced by factors such as the manufacturing environment, product design, production system, and overall cost considerations. These factors directly impact the decision-making process. The ultimate goal for the decision maker is to pinpoint and choose the most suitable robot, capable of delivering the desired output while minimizing costs and catering to the specific requirements of the industry. So, to consider it, in this paper, the hybrid structure of the Aczel-Alsina (AA) and Bonferroni mean (BM) operators for interval-valued intuitionistic fuzzy (IVIF) environment has been proposed, which can show the interrelationship between the multiple criteria and assist the expertise in decision-making (DM) process. Moreover, the algorithm and methodology for the multi-criteria group decision-making (MCGDM) problem have been defined which is further utilized by solving a real-world problem to demonstrate the effectiveness and validity of the proposed method. At last, the comparison analysis between prior and proposed studies has been displayed, and then followed by the conclusion of the result.

An extended ITARA-TOPSIS method for multi-criteria group decision-making problems based on R-number

With the continuous improvement and development of various decision-making methods, it has led to the widespread use of fuzzy sets and fuzzy numbers. At the same time, the application of decision-making methods in different fuzzy environments has been very effective in addressing the deficiencies in existing research. At present, triangular fuzzy numbers have been widely used in the evaluation aspects of various decision making methods, and the proposed R-number effectively solve the uncertainty involving problems related to future events, but the existing research based on the TOPSIS method in the R-number environment has not yet been clearly applied to the triangular fuzzy number environment, and the indifference threshold-based attribute ratio analysis (ITARA) method in the fuzzy environment has yet to be extended. Therefore, this paper proposes a fuzzy indifference threshold-based attribute ratio analysis (FITARA) method based on triangular fuzzy numbers for solving the problem of determining attribute weights in the multi-attribute decision-making process. Secondly, the various risks of the decision environment and the impact on future events are considered and R-number are used to solve this puzzle. In addition, the incorporation of risk perception factors in the context of the existing RTOPSIS method considering multiple risk factors and the use of Manhattan distances to optimize the large number of operations in the process of the method resulted in the development of the FITARA-RTOPSIS model. Finally, the proposed FITARA-RTOPSIS method is applied to the problem of siting emergency supplies storage depots, and the effectiveness of the proposed method is verified through comparative analysis.

A multi-criteria group decision-making method with fuzzy preference relations based on filtration-and-weighting-based triangular bounded consistency

In multi-criteria group decision-making (MCGDM) problems with incomplete fuzzy preference relations (FPRs), the consistency based on bounded rationality is preferred to depend on the historical preferences of decision makers to generate complete FPR matrices. There are two factors in influencing the effect of historical preferences on complete FPR matrices and further decision makers’ satisfaction of group solutions. One is the effectiveness of historical preferences and the other is their relative weights. On this basis, this paper proposes a new MCGDM method with FPRs based on the filtration-and-weighting-based triangular bounded consistency (FWBTBC), where historical FPRs between three adjacent pairs of alternatives are characterized by triangles and these two factors are considered comprehensively. A triangle filtration process is designed based on the Grubbs criterion to filter the abnormal triangles in the collected ones. A weight determination process is developed, where a distance measure between remaining triangles is constructed to calculate their weights. Based on the combination of the two processes, the FWBTBC of FPRs is created and then the proposed method is presented. The validity of the proposed method is demonstrated by its application in analyzing a drainage tube supplier selection problem for a tertiary hospital located in Hefei, Anhui, China.

An interval type-2 fuzzy best-worst method and likelihood-based multi-criteria method in group decision-making

In real-world decision-making problems, a group of decision-makers (DMs) with different levels of expertise gathers to investigate the problem from various perspectives. Making the best choice from an analogous shortlist of competitors is challenging, even for an expert group. To address these types of problems, a new multi-criteria group decision-making (MCGDM) methodology under the interval type-2 trapezoidal fuzzy (IT2TrF) environment is proposed. The proposed IT2TrF MCGDM method comprises three phases. In the first phase, the IT2TrF cognitive best-worst method (IT2TrF-CBWM) is introduced to calculate the initial weights of criteria using the interval scale. Subsequently, a new consistency index (CI) and consistency ratio (CR) are presented. In the second phase, an optimization model is proposed to determine the final IT2TrF weights of criteria. Finally, a likelihood-based method for solving MCGDM problems is introduced in the third phase. The validity of the proposed method is illustrated by addressing a healthcare waste (HCW) treatment technology selection problem during the COVID-19 pandemic. Sensitivity and comparative analyses highlight the superiority and effectiveness of the presented MCGDM method.

Retracted: Novel Distance Measures for Single-Valued Neutrosophic Fuzzy Sets and Their Applications to Multicriteria Group Decision-Making Problem

Retracted: Novel Distance Measures for Single-Valued Neutrosophic Fuzzy Sets and Their Applications to Multicriteria Group Decision-Making Problem

Combining grey relation analysis with MCGDM to evaluate the higher education management quality with interval-valued neutrosophic sets

With the continuous deepening of higher education management reform, university leaders have realized that the merger of universities, annual expansion of enrollment, and expansion of educational scale have broadened the development space for universities. At the same time, many management problems have also emerged, and education management problems are particularly prominent, such as some decisions, plans, instructions, etc. of the school level education management department not being well implemented in various departments, and the channels for the school level education management department to understand the true situation of each department are not smooth. Therefore, deepening reform provides a good opportunity for universities to strengthen management and streamline relationships. Teaching and scientific research must be upgraded, and the quality of teaching management must be improved. Establishing an education management quality evaluation system and emphasizing the quality of education management work are the key. The higher education management quality evaluation is affirmed as multi-criteria group decision-making (MCGDM). Interval-valued neutrosophic sets (IVNSs) have been widely used and researched in MCGDM. The interval-valued neutrosophic sets (IVNSs) could depict the uncertain information within the higher education management quality evaluation. The purpose of this article is to proposed a new improved grey relation analysis (GRA) method based on prospect theory (PT-GRA) to solve the MCGDM under IVNSs. At the end of this paper, an example for higher education management quality evaluation is illustrated through the built method and the comparison. Thus, the main contribution of this study is: (1) the PT-GRA method is used to deal with the MCGDM problems under IVNSs; (2) the weight information is obtained through entropy method; (3) an empirical example for higher education management quality evaluation has been given. (4) some comparative algorithms are given to show the rationality of PT-GRA method with IVNSs.

MABAC method based on cumulative prospect theory for MCGDM with dual probabilistic linguistic term set and applications to sustainable supplier selection

Dual probabilistic linguistic term set (DPLTS) is a new proposed decision-making environment. It uses probabilistic form to represent the appraisal of the alternative from decision makers. There are few methods to deal with DPLTS according to the literature proposed up to now. The purpose of this article is to proposed a new improved Multi-Attribute Border Approximation Area Comparison (MABAC) method extended by cumulative prospect theory (CPT) and combined with DPLTS to address the multi-criteria group decision-making (MCGDM) problem of sustainable supplier selection. In order to make the decision procedure containing more fuzzy information, we also improved the equation of distance between DPLTSs with system of rectangular coordinates. This new improved MABAC method is combined with CPT and it is semi-objective method. Not only in the procedure of calculating distance between alternatives and border approximation area, but also in the procedure of determining the weights of attributes. At the end of this paper, the comparison of this new method with other proposed DPLTS methods, such as Correlation Coefficient Method and DPLTS-TODIM-CRITIC Method, demonstrates the availability and difference.

Three-way group decision based on regret theory under dual hesitant fuzzy environment: An application in water supply alternatives selection

For actual multi-criteria group decision-making (MCGDM) issues with complexity and uncertainty, decision-makers may not be completely rational, and the psychological characteristics generally exert influences on the decision process. As an effective cognitive model, three-way decision (TWD) dedicates to handling uncertainty and is widely used in distinct fields. In this regard, this study incorporates regret emotion into TWD in the dual hesitant fuzzy (DHF) context, and accordingly designs a decision model for uncertain MCGDM issues considering bounded rationality. Specifically, by means of distance measures and score functions of dual hesitant fuzzy elements (DHFEs), the calculation method of loss functions and conditional probability are proposed firstly. Meanwhile, drawing from regret theory, the TWD rules considering regret emotion are generated under the DHF environment. Further, based on this, a detailed three-way group decision model based on regret theory, aimed at solving MCGDM problems under DHF uncertainty, water supply alternatives selection, is constructed. Lastly, a numerical example is employed to elaborate the application of the model.

An indirect multicriteria group decision-making method with heterogeneous preference relations and reliabilities of decision-makers

This study proposes a new indirect method to solve multicriteria group decision-making (MCGDM) problems with heterogeneous preference relations and decision-makers’ reliabilities. To unify the heterogeneous preference relations, the transformation of multiplicative preference relations (MPRs), fuzzy preference relations (FPRs), intuitionistic fuzzy preference relations (IFPRs), and linguistic preference relations (LPRs) into distributed preference relations (DPRs) is analyzed. As consistency among DPRs is constructed under the assumption that decision-makers are bounded rationality, the abstract transformation of MPR, FPR, IFPR, and LPR into DPR is defined, and its reality depends on the preferences of decision-makers. Two important properties of abstract transformation, namely, internal consistency and restricted max-max transitivity, were theoretically verified. The reliabilities of decision-makers are involved in MCGDM by estimating the reliability of each criterion to improve solution quality. Based on the four types of abstract transformations, a process for analyzing MCGDM problems with heterogeneous preference relations and decision-makers’ reliabilities is developed. The proposed method is used to analyze a new business selection problem for an enterprise located in Changzhou, Jiangsu, China to demonstrate its applicability and validity.

An investigation of ambiguous sets and their application to decision-making from partial order to lattice ambiguous sets

The idea of ambiguous set (AS) theory has been introduced to describe the uncertainties, imprecisions and haziness innate in information. This study generalizes the notion of AS to a single-valued ambiguous number (SVAN). We propose the concepts of partial ambiguous order set (PAOS) and lattice ambiguous set (LAS) for SVANs. Two operators, namely A-norms and A-conorms, are proposed for LAS. In this study, a degree of fitness function (DFF) and an ambiguous weighted geometric operator (AWGO) are also introduced to compare and aggregate the events in the form of SVANs. We propose a method based on A-norms, A-conorms and AWGO for solving multi-criteria group decision-making (MCGDM) problems. Finally, a real-time example of a MCGDM problem associated with the selection of cell phones by customers is presented, and its solution is suggested using the proposed method.

A hybrid approach based on dual hesitant q-rung orthopair fuzzy Frank power partitioned Heronian mean aggregation operators for estimating sustainable urban transport solutions

Transportation systems are a key part of sustainable development, and they need to be carefully evaluated to show that they have a strong impact on the target area’s social, environmental, and economic sustainability. For this reason, involving the developed decision support systems helps to shed light on the users’ demand and provide unblemished policy decisions considering the existing situation. The “q-rung orthopair fuzzy set (q-ROFS)” is a generalization of the “intuitionistic fuzzy sets (IFSs)” and “Pythagorean fuzzy sets (PFSs)” that expresses vague and uncertain data more efficiently. In the interim, the notion of “dual hesitant q-rung orthopair fuzzy set (DHq-ROFS)” is presented to account for human hesitancy, which may be more applicable to genuine “multicriteria group decision-making (MCGDM)” situations. The main goal of this study is to address MCGDM problems using Heronian mean (HM) and DHq-ROF data. The first step is to introduce the Frank t-norm and t-conorm-based DHq-ROF HM (DHq-ROFFHM) operator. DHq-ROFFHM’s features are next described in depth. In addition, the DHq-ROF Frank weighted HM (DHq-ROFFWHM) operator is presented, which takes into account different degrees of liking for input arguments. The DHq-ROF Frank weighted power partitioned HM model is then used to come up with a way to solve models in MCGDM problems where individual arguments are grouped together and have relationships with each other. A final example shows how the established model can be implemented and how well it works.

A general model of ambiguous sets to a single-valued ambiguous numbers with aggregation operators

The ambiguous sets have recently been proposed to represent inherent uncertainties, imprecision, and vague information. In this study, we generalize the concept of the ambiguous set to a single-valued ambiguous number (SVAN). We propose many comparison functions and operational laws for SVANs. This study also introduces three new aggregation operators, the ambiguous weighted geometric operator (AWGO), the ambiguous ordered weighted geometric operator (AOWGO), and the ambiguous hybrid geometric operator (AHGO), for aggregating the input information in the form of SVANs. We discuss some significant properties of the operators along with numerical examples. We develop a method based on the AWGO and AHGO for solving multi-criteria group decision-making (MCGDM) problems. Finally, a real-time example of a MCGDM problem associated with the selection of cars by customers is presented, and its solution is recommended using the proposed method.