Fuzzy Multiple Criteria Group Decision Research Articles

Solution strategy for sustainable additive manufacturing design problem using Pythagorean fuzzy MCGDM methodology

To solve difficulties involving various groups’ decision-making problems, this work has been proposed to develop a logical aggregation approach to aggregate decision-makers’ crisp data into Pythagorean fuzzy numbers. By combining the established strategy with the Pythagorean fuzzy TOPSIS method, a hybrid Pythagorean fuzzy multiple criteria group decision-making methodology is presented. Based on fuzzy rules inference and the Takagi–Sugeno technique, a novel function is created to represent the degrees of uncertainty in decision-makers’ data. As an example, the material selection process in practical additive manufacturing designs is provided to show how the proposed methodology may be applied to actual applications. Sensitivity analysis is used to evaluate the effectiveness of the suggested methodology. The outcomes demonstrate that the plan was successful in producing a PFN that accurately reflects the decision-maker’s knowledge.

The differential measure for Pythagorean fuzzy multiple criteria group decision-making

Pythagorean fuzzy sets (PFSs) proved to be powerful for handling uncertainty and vagueness in multi-criteria group decision-making (MCGDM). To make a compromise decision, comparing PFSs is essential. Several approaches were introduced for comparison, e.g., distance measures and similarity measures. Nevertheless, extant measures have several defects that can produce counter-intuitive results, since they treat any increase or decrease in the membership degree the same as the non-membership degree; although each parameter has a different implication. This study introduces the differential measure (DFM) as a new approach for comparing PFSs. The main purpose of the DFM is to eliminate the unfair arguments resulting from the equal treatment of the contradicting parameters of a PFS. It is a preference relation between two PFSs by virtue of position in the attribute space and according to the closeness of their membership and non-membership degrees. Two PFSs are classified as identical, equivalent, superior, or inferior to one another giving the degree of superiority or inferiority. The basic properties of the proposed DFM are given. A novel method for multiple criteria group decision-making is proposed based on the introduced DFM. A new technique for computing the weights of the experts is developed. The proposed method is applied to solve two applications, the evaluation of solid-state drives and the selection of the best photovoltaic cell. The results are compared with the results of some extant methods to illustrate the applicability and validity of the method. A sensitivity analysis is conducted to examine its stability and practicality.

Comparative Analysis of Hybrid Fuzzy MCGDM Methodologies for Optimal Robot Selection Process

The generalized interval-valued trapezoidal fuzzy best-worst method (GITrF-BWM) provides more reliable and more consistent criteria weights for multiple criteria group decision making (MCGDM) problems. In this study, GITrF-BWM is integrated with the extended TOPSIS (technique for order preference by similarity to the ideal solution) and extended VIKOR (visekriterijumska optimizacija i kompromisno resenje) methods for the selection of the optimal industrial robot using fuzzy information. For a criteria-based selection process, assigning weights play a vital role and significantly affect the decision. Assigning weights based on direct opinions of decision makers can be biased, so weight deriving models, such as GITrF-BWM, overcome this discrepancy. In previous studies, generalized interval-valued trapezoidal fuzzy weights were not derived by using any MCGDM method for the robot selection process. For this study, both subjective and objective criteria are considered. The preferences of decision makers are provided with the help of linguistic terms that are then converted into fuzzy information. The stability and reliability of the methods were tested by performing sensitivity analysis, which showed that the ranking results of both the methodologies are not symmetrical, and the integration of GITrF-BWM with the extended TOPSIS method provides stable and reliable results as compared to the integration of GITrF-BWM with the extended VIKOR method. Hence, the proposed methodology provides robust optimal industrial robot selection.

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.

Intuitionistic Fuzzy Multiple Criteria Group Decision Making: A Consolidated Model With Application to Emergency Plan Selection

With complexity and uncertainty having an increasing impact on the decision-making environment, much attention is being paid to the development and application of multiple criteria group decision-making (MCGDM) models owing to the potential for fully exploiting the diverse strengths and expertise of various members. In general, inevitable interactions among decision makers (DMs), when a number of DMs share similar knowledge and experiences, can have a significant impact on the management of decision information directly or indirectly related to DMs, and can easily lead to distorted and unconvincing decision outcomes. In order to model the MCGDM problem in which DMs share a similar background, a consolidated MCGDM model in the context of intuitionistic fuzzy sets (IFSs) is developed. First, we refine the constructive principles for intuitionistic fuzzy entropy (IFE) and use them as a basis to produce a novel IFE measure simultaneously factoring in the intuitionism and fuzziness of IFSs. With the aim of dealing with the impact on the specifications of the weights of DMs and criteria, an integrated method is then proposed based on the novel IFE measure, 2-additive fuzzy measure, and Choquet integral. Due to their capability of modeling effectively the interrelationships among arguments, the weighted intuitionistic fuzzy Bonferroni mean (WIFBM) and the weighted intuitionistic fuzzy geometric Bonferroni mean (WIFGBM) are introduced to fuse the individual evaluation values of alternatives on criteria. In addition, simple additive weighting based on the WIFBM or WIFGBM is applied to rank alternatives and select the best one. Finally, the feasibility and effectiveness of the proposed model are explored with a case study of an emergency plan decision-making problem accompanied with sensitivity and comparison analysis.

A Multi-Criteria Group Decision Making Model for Green Supplier Selection under the Ordered Weighted Hesitant Fuzzy Environment

The green supplier selection (GSS) problem is one of the most pressing issues that can directly affect manufacturer performance. GSS has been studied in previous literature, which is considered to be a typical multiple criteria group decision making (MCGDM) problem. The ordered weighted hesitant fuzzy MCGDM method can present the importance of each possible value, and the priority relationship among criteria has rarely been studied. In this study, we first extend the prioritized average (PA) operator to the ordered weighted hesitant fuzzy set (OWHFS) for solving the both problems. The generalized ordered weighted hesitant fuzzy prioritized weighted average operator (GOWHFPWA) is recommended, and some desirable properties are discussed. Based on this operator, a novel MCGDM method for GSS is developed. A numerical example of GSS is then given to prove the robustness of the proposed approach, and a sensitivity analysis is used to identify the robustness of the proposed method. Finally, a comparative analysis based on the MCGDM approach with the hesitant fuzzy prioritized weighted average (HFPWA) operator is illustrated to indicate the validity and advantages of the proposed approach.

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.

Tackling Complex Emergency Response Solutions Evaluation Problems in Sustainable Development by Fuzzy Group Decision Making Approaches with Considering Decision Hesitancy and Prioritization among Assessing Criteria

In order to be prepared against potential balance-breaking risks affecting economic development, more and more countries have recognized emergency response solutions evaluation (ERSE) as an indispensable activity in their governance of sustainable development. Traditional multiple criteria group decision making (MCGDM) approaches to ERSE have been facing simultaneous challenging characteristics of decision hesitancy and prioritization relations among assessing criteria, due to the complexity in practical ERSE problems. Therefore, aiming at the special type of ERSE problems that hold the two characteristics, we investigate effective MCGDM approaches by hiring interval-valued dual hesitant fuzzy set (IVDHFS) to comprehensively depict decision hesitancy. To exploit decision information embedded in prioritization relations among criteria, we firstly define an fuzzy entropy measure for IVDHFS so that its derivative decision models can avoid potential information distortion in models based on classic IVDHFS distance measures with subjective supplementing mechanism; further, based on defined entropy measure, we develop two fundamental prioritized operators for IVDHFS by extending Yager’s prioritized operators. Furthermore, on the strength of above methods, we construct two hesitant fuzzy MCGDM approaches to tackle complex scenarios with or without known weights for decision makers, respectively. Finally, case studies have been conducted to show effectiveness and practicality of our proposed approaches.

A Novel Approach Based on Similarity Measure for Pythagorean Fuzzy Multiple Criteria Group Decision Making

The Pythagorean fuzzy set, as a new extension of intuitionistic fuzzy set, has recently been developed to manage the complex uncertainty in practical group decision problems. The purpose of this article is to develop a new decision method based on similarity measure to address multiple criteria group decision making problems within Pythagorean fuzzy environment based on Pythagorean fuzzy numbers (PFNs). The contribution of this article is fivefold: (1) An accuracy function of PFNs is defined and a new ranking method for PFNs is proposed; (2) new Pythagorean fuzzy aggregating operators are developed; (3) a novel similarity measure for PFNs is presented, and some desirable properties are discussed; (4) a simple and effective Pythagorean fuzzy group decision method is introduced; and (5) The proposed method is applied to address the selection problem of photovoltaic cells.

Some Hesitant Fuzzy Information Aggregation Operators Based on Einstein Operational Laws

The performance and development review (PADR) evaluation in a company is a complex group decision-making problem that is influenced by multiple and conflicting objectives. The complexity of the PADR evaluation problem is often due to the difficulties in determining the degrees of an alternative that satisfies the criteria. In this paper, we present a hesitant fuzzy multiple criteria group decision-making methods for PADR evaluation. We first develop some operations based on Einstein operations. Then, we proposed some aggregation operators to aggregate hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about PADR evaluation in a company is provided to illustrate the developed method.

Intuitionistic Trapezoidal Fuzzy Multiple Criteria Group Decision Making Method Based on Binary Relation

The aim of this paper is to develop a methodology for intuitionistic trapezoidal fuzzy multiple criteria group decision making problems based on binary relation. Firstly, the similarity measure between two vectors based on binary relation is defined, which can be utilized to aggregate preference information. Some desirable properties of the similarity measure based on fuzzy binary relation are also studied. Then, a methodology for fuzzy multiple criteria group decision making is proposed, in which the criteria values are in the terms of intuitionistic trapezoidal fuzzy numbers (ITFNs). Simple and exact formulas are also proposed to determine the vector of the aggregation and group set. According to the weighted expected values of group set, it is easy to rank the alternatives and select the best one. Finally, we apply the proposed method and the Cosine similarity measure method to a numerical example; the numerical results show that our method is effective and practical.

Extended VIKOR method based on cross-entropy for interval-valued intuitionistic fuzzy multiple criteria group decision making

With respect to multiple criteria group decision making problems with conflicting and non-commensurable criteria, it is generally difficult to find an alternative that meets all the criteria simultaneously. By extending the fuzzy VIKOR method, this study provides a rational and systematic process for developing the best alternative and compromise solution under the interval-valued intuitionistic fuzzy environment. Furthermore, a fuzzy cross-entropy approach is proposed to state the discrimination measure between optional and optimal interval-valued intuitionistic fuzzy numbers. Finally, to expatiate on the practical value of the method proposed, an illustrative example is presented to demonstrate its practicality and effectiveness over existing TOPSIS method.

A hybrid fuzzy multiple criteria group decision making approach for sustainable project selection

In this paper, a new hybrid fuzzy multiple criteria group decision making (FMCGDM) approach has been proposed for sustainable project selection. First, a comprehensive framework, including economic, social, and environmental effects of an investment, strategic alliance, organizational readiness, and risk of investment has been proposed for sustainable project selection. As the relative importance of the criteria of the proposed framework are hard to find through several conflictive preferences of a group of Decision Makers (DMs) so, a goal programming (GP) has been supplied to this aim considering multiplicative and fuzzy preference relation. Then, a fuzzy TOPSIS method has been developed to assess the fitness of investment chances. It is based on Preference Ratio (PR), which is known as an efficient ranking method for fuzzy numbers, and a fuzzy distance measurement. The properties of proposed hybrid approach make it robust for modeling real case of uncertain group decision making problems. The FMCGDM has been developed through a linkage between Lingo 11.0, MS-Excel 12.0, and Visual Basic 6.0. The proposed hybrid approach has been applied in a real case study called Iranian financial and credit institute for sustainable project selection.

Application of a fuzzy TOPSIS method base on modified preference ratio and fuzzy distance measurement in assessment of traffic police centers performance

In this paper we have presented a TOPSIS approach based on preference ratio and an efficient fuzzy distance measurement for a Fuzzy Multiple Criteria Group Decision-Making Problem (FMCGDMP). Preference ratio with a moderate modification for negative fuzzy numbers was used as an efficient ranking method for fuzzy numbers in a relative manner. As human reasoning persuades that distances between two fuzzy numbers should be a fuzzy measure, so all distances between fuzzy numbers (i.e. distances between alternatives, Fuzzy Positive Ideal solutions, and Fuzzy Negative Ideal solutions) have been calculated as fuzzy numbers using an efficient fuzzy distance measurement. The aforementioned arguments make the proposed algorithm unique and well posed for real-life problem modeling. Moreover, the main novelties of the proposed procedure (i.e. the fuzzy distance measurement and Preference Ratio) have been developed for Generalized Fuzzy Numbers (GFNs). The proposed algorithm has efficiently been applied in assessment of traffic police centers which is treated as a FMCGDMP.

Generalizing TOPSIS for fuzzy multiple-criteria group decision-making

In this paper, we generalize TOPSIS to fuzzy multiple-criteria group decision-making (FMCGDM) in a fuzzy environment. TOPSIS is one of the well-known methods for multiple-criteria decision-making (MCDM). Most of the steps of TOPSIS can be easily generalized to a fuzzy environment, except max and min operations in finding the ideal solution and negative ideal solution. Thus we propose two operators Up and Lo which satisfy the partial ordering relation on fuzzy numbers to the generalization of TOPSIS. In generalized TOPSIS, these two operations (Up and Lo) are employed to find ideal and negative ideal solutions under a fuzzy environment. Then the FMCGDM problem can be solved effectively and efficiently.