A new soft computing model based on linear assignment and linear programming technique for multidimensional analysis of preference with interval type-2 fuzzy sets

Multiple criteria decision making (MCDM) approach plays an important role in life, since it is always necessary to make decisions through various alternatives based on specific criteria. In this paper, interval type-2 fuzzy sets (IT2FSs) are used because in most cases in the real-world the information is incomplete and ambiguous. A new group decision approach with linear assignment method (LAM) is proposed. In addition, weight of each evaluation factor according to subjective and objective data is constructed based on a new developed version of linear programming technique for multidimensional analysis of preference (LINMAP) method. In the proposed method, weights of decision makers (DMs) are computed based on a novel approach that applies a new modified method based on the concept of ideal solutions. Furthermore, a new IT2F-ranking method is introduced. To display the applicability of the presented soft computing method, firstly, a real case study of green supplier selection problem is adopted from the literature and solved. Moreover, the method is applied in a second case study of project evaluation and selection problem. Two applications show that the introduced method presents a proper soft computing framework that can handle real-world uncertain environments. Moreover, the method can consider importance of the DMs and evaluation criteria.     

Regret theory-based group decision-making with multidimensional preference and incomplete weight information

In this paper, we study fuzzy multi-attribute group decision-making (FMAGDM) problems with multidimensional preference information in the form of pairwise alternatives and incomplete weight information. We develop a new group decision-making (GDM) method considering regret aversion of the decision-makers (DMs). Firstly, we define a fuzzy regret/rejoice function and a computational formula for the perceived utility of alternative decisions. We propose a perceived utility value-based group consistency index (which reflects the total consistency) and a group inconsistency index (which represents the total inconsistency) for pairwise rankings of alternatives based on regret theory and an a priori multidimensional preference order given by the DMs. Then, under the circumstances of an unknown fuzzy ideal solution, we set up a mathematical programming model to determine the optimal attribute weights and a defuzzified fuzzy ideal solution with the idea of the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP). We compute the DMs’ optimal comprehensive perceived utility values and obtain the ranking order of alternatives. Finally, we illustrate the application of the developed procedures with an air-fighter selection problem. The rationality and validity of the proposed method is demonstrated by comparing with two other GDM methods, including the fuzzy LINMAP (FLINMAP) method and the prospect theory-based GDM method.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

On group decision making with four formats of incomplete preference relations

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in four formats of incomplete preference relations, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations, incomplete additive linguistic preference relations, incomplete multiplicative linguistic preference relations. In order to make the collective opinion close each decision maker’s opinion as near as possible, an optimization model is constructed to integrate the four different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.     

Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives

The aim of this study is to propose a Fuzzy multi-criteria decision-making approach (FMCDM) to evaluate the alternative options in respect to the user's preference orders. Two FMCDM methods are proposed for solving the MCDM problem: Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine the relative weights of the evaluation criteria and the extension of the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) is applied to rank the alternatives. Empirical results show that the proposed methods are viable approaches in solving the problem. When the performance ratings are vague and imprecise, this Fuzzy MCDM is a preferred solution.     

A goal programming approach to group decision-making with three formats of incomplete preference relations

This paper proposes a goal programming approach to solve the group decision-making problem where the preference information about alternatives provided by decision makers can be represented in three formats, i.e., incomplete multiplicative preference relations, incomplete fuzzy preference relations and incomplete linguistic preference relations. In the approach, a transformation function is introduced to transform the incomplete linguistic preference relation into an incomplete fuzzy preference relation. To narrow the gap between the collective opinion and each decision maker’s opinion, a liner goal programming model is constructed to integrate the three different formats of incomplete preference relations and to compute the collective ranking values of the alternatives. Thus, the ranking order of alternatives or selection of the most desirable alternative(s) is obtained directly according to the computed collective ranking values. A numerical example is also used to illustrate the feasibility and the applicability of the proposed approach.     

Pythagorean fuzzy TOPSIS for multicriteria group decision-making with unknown weight information through entropy measure

In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)-based methodology is proposed to solve multicriteria group decision-making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision-making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.     

A new linguistic MCDM method based on multiple-criterion data fusion

Multiple-criteria decision-making (MCDM) is concerned with the ranking of decision alternatives based on preference judgements made on decision alternatives over a number of criteria. First, taking advantage of data fusion technology to comprehensively consider each criterion data is a reasonable idea to solve the MCDM problem. Second, in order to efficiently handle uncertain information in the process of decision making, some well developed mathematical tools, such as fuzzy sets theory and Dempster Shafer theory of evidence, are used to deal with MCDM. Based on the two main reasons above, a new fuzzy evidential MCDM method under uncertain environments is proposed. The rating of the criteria and the importance weight of the criteria are given by experts’ judgments, represented by triangular fuzzy numbers. Then, the weights are transformed into discounting coefficients and the ratings are transformed into basic probability assignments. The final results can be obtained through the Dempster rule of combination in a simple and straight way. A numerical example to select plant location is used to illustrate the efficiency of the proposed method.     

In search of best alternatives: a TOPSIS driven MCDM procedure for neural network modeling

Multiple criteria decision making (MCDM) is an approach to rank the alternatives with respect to the different attributes. Several MCDM approaches were used to select the best alternatives of meta-heuristic modeling under the soft-computing domain where the true best alternative is not known. Alternatives are artificial neural network models, selection of which is difficult based on many conflicting performance measures. This paper addresses two new methods for MCDM, using the concept of Minkowski distance and based on technique for order preference by similarity to ideal solution philosophy. The performances of these two methods are compared with four other methods considering real-life data and simulated experiments.     

Extension of the ELECTRE method based on interval-valued fuzzy sets

Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection problem.     

An interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions and its application to multiple criteria decision analysis

This paper presents an interval-valued intuitionistic fuzzy permutation method with likelihood-based preference functions for managing multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets. First, certain likelihood-based preference functions are proposed using the likelihoods of interval-valued intuitionistic fuzzy preference relationships. Next, selected practical indices of concordance/discordance are established to evaluate all possible permutations of the alternatives. The optimal priority order of the alternatives is determined by comparing all comprehensive concordance/discordance values based on score functions. Furthermore, this paper considers various preference types and develops another interval-valued intuitionistic fuzzy permutation method using programming models to address multiple criteria decision-making problems with incomplete preference information. The feasibility and applicability of the proposed methods are illustrated in the problem of selecting a suitable bridge construction method. Moreover, certain comparative analyses are conducted to verify the advantages of the proposed methods compared with those of other decision-making methods. Finally, the practical effectiveness of the proposed methods is validated with a risk assessment problem in new product development.     

Consensus reaching process for group decision-making based on trust network and ordinal consensus measure

Due to the urgent nature of emergency decision making, it is necessary to reach the consensus requirement quickly. Ordinal consensus measure explores the relation between the rankings and helps to intuitively know which alternative needs to be adjusted to accelerate the improvement of consensus. Moreover, decision makers (DMs) in the decision making problem are often connected through trust relationships which affect the DMs’ judgments in the process of DMs’ interaction. Therefore, this paper explores trust network-based group decision-making in which the consensus level is estimated by an ordinal consensus measure. We first focus on the supplementation of an incomplete trust network. One of the most common methods is to design the trust propagation operator, whereas the intensity of information propagation may be different in various scenarios. Therefore, considering the different numerical scale of the linguistic term set, a trust propagation operator with different intensity of trust propagation is designed to obtain the indirect trust relationship. In the process of supplementing the incomplete trust network, the contribution of DMs to propagating information is concerned, which can be described by the betweenness centrality, and the importance weights of DMs are determined by combining the betweenness centrality and trust in-degree. In the consensus reaching process, we first propose an improved ordinal consensus measure, which takes into account the consistency of orders of the same alternative in different rankings as well as the importance of positions of alternatives. Then, we design the identification rule and the feedback mechanism for those with low consensus levels. The identification rule is used to select the DMs which first few alternatives in the ranking are different with those in the ranking of group. And in the feedback mechanism, the referenced preference relation (FPR) obtained by the trust network is provided for the identified DMs. Afterwards, combining the referenced FPR, an optimization model is designed to give the adjustment opinion. Finally, a numerical example elaborates on the feasibility of the trust propagation operator and consensus model. The comparative analysis demonstrates the rationality and effectiveness of the proposed model.     

Group decision making procedure considering preference strength under incomplete information

This article deals with the multiple criteria decision making problem with incomplete information when multiple decision makers (Multiple Criteria Group Decision Making: MCGDM) are involved. Usually decision makers (DMs) are willing or able to provide only incomplete information, because of time pressure, lack of knowledge or data, and their limited expertise related to the problem domain. There have only been a few studies considering incomplete information in group settings. We also consider the case where importance weights are given incompletely. This article suggests the possibility that individually optimized results can be used to build group consensus. Individual optimization results by pairwise dominance, contain useful information in forming consensus, such as, ordinal rankings or preference intensity of an alternative over the others. Rather than using ordinal rankings for aggregation which do not consider preference strength, we suggest a procedure that takes account of individual DMs' preference strength.     

A Model for Decision Making with Missing,Imprecise, and Uncertain Evaluations of Multiple Criteria

In real‐life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval‐valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria's evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster's rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret‐avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real‐life MCDM problems.     

Extension of Fuzzy ELECTRE based on VIKOR method

Many decision problems in real-world deal with conflicting criteria, uncertainty and imprecise information. Some also allow a group of decision makers (DMs) to make their opinions independently. Multi-criteria decision making (MCDM) is a well known decision method that can make the quality of group multiple criteria decisions better by creating a more explicit, rational and efficient process. A group of MCDM models known as “outranking methods” have been used to rank a set of alternatives. ELECTRE I is an outranking method which is simple, but provides partial ranking. So we consider VIKOR and try to mitigate this problem with regard to relations between VIKOR and ELECTRE. The objective of this paper is to extend ELECTRE I method based on VIKOR to rank a set of alternatives versus a set of criteria to show the decision maker’s preferences.     

A new multi criteria decision making approach for medical imaging systems considering risk factors

Effective and good quality imaging is important for medical decision-making and can reduce unnecessary costs and procedures. Therefore, decision making regarding any technology can present serious problems for healthcare centers with multi criteria decision making problems (MCDM). This paper is the first to develop the fuzzy axiomatic design with risk factors (RFAD) approach and to use it in multi attribute comparisons of medical imaging systems in a university hospital. Although most MCDM approaches in the literature treat risk factors as separate criteria, in real life every alternative has its own risks related to each criterion. The proposed approach integrates the risk factors in each criterion and calculates the information content to compare alternatives. This paper applies three different approaches to MCDM problems related to the selection of medical imaging systems for a university hospital.     

Prioritized multi-criteria decision making based on preference relations

There may exist priority relationships among criteria in multi-criteria decision making (MCDM) problems. This kind of problems, which we focus on in this paper, are called prioritized MCDM ones. In order to aggregate the evaluation values of criteria for an alternative, we first develop some weighted prioritized aggregation operators based on triangular norms (t-norms) together with the weights of criteria by extending the prioritized aggregation operators proposed by Yager (Yager, R. R. (2004). Modeling prioritized multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 34, 2396–2404). After discussing the influence of the concentration degrees of the evaluation values with respect to each criterion to the priority relationships, we further develop a method for handling the prioritized MCDM problems. Through a simple example, we validate that this method can be used in more wide situations than the existing prioritized MCDM methods. At length, the relationships between the weights associated with criteria and the preference relations among alternatives are explored, and then two quadratic programming models for determining weights based on multiplicative and fuzzy preference relations are developed.     

Group decision-making model with incomplete fuzzy preference relations based on additive consistency.

In decision-making problems there may be cases in which experts do not have an in-depth knowledge of the problem to be solved. In such cases, experts may not put their opinion forward about certain aspects of the problem, and as a result they may present incomplete preferences, i.e., some preference values may not be given or may be missing. In this paper, we present a new model for group decision making in which experts' preferences can be expressed as incomplete fuzzy preference relations. As part of this decision model, we propose an iterative procedure to estimate the missing information in an expert's incomplete fuzzy preference relation. This procedure is guided by the additive-consistency (AC) property and only uses the preference values the expert provides. The AC property is also used to measure the level of consistency of the information provided by the experts and also to propose a new induced ordered weighted averaging (IOWA) operator, the AC-IOWA operator, which permits the aggregation of the experts' preferences in such a way that more importance is given to the most consistent ones. Finally, the selection of the solution set of alternatives according to the fuzzy majority of the experts is based on two quantifier-guided choice degrees: the dominance and the nondominance degree.     

A new fuzzy weighted average (FWA) method based on left and right scores: An application for determining a suitable location for a gas oil station

The selection of a facility location from alternative locations is a multiple criteria decision making (MCDM) problem including both quantitative and qualitative criteria. In many real-life cases, determining the exact values for MCDM problems, and especially for facility location selection problems, is difficult or impossible, so the values of alternatives with respect to the criteria or/and the values of criteria weights are considered as fuzzy values (fuzzy numbers) such that the conventional crisp approaches for solving facility location selection problems and other MCDM problems tend to be less effective for dealing with the imprecise or vagueness nature of the linguistic assessments. In such conditions, fuzzy MCDM methods are applied for facility location selection problem and other fuzzy MCDM problems. In this paper, we propose a new fuzzy weighted average (FWA) method based on left and right scores for fuzzy MCDM problems. Moreover, we apply the proposed method to a real application. As a result, we found that the proposed method is practical for facility location selection problems. Besides, it seems that the proposed FWA method is very accurate, flexible, simple, and easy to use when compared to other versions of the FWA method.     

Deriving priority weights from intuitionistic fuzzy multiplicative preference relations

Intuitionistic fuzzy multiplicative preference relations (IFMPRs), as an extension of multiplicative preference relations, can denote the decision-makers’ (DMs’) preferred and nonpreferred degrees simultaneously. Just as any other type of preference relations, consistency is crucial to guarantee the rational ranking orders. Thus, this paper introduces a new consistent concept for IFMPRs that is a natural extension of crisp case and overcomes the issues in the previous concepts of consistency. To judge the consistency of IFMPRs, several programming models are constructed, and an approach to deriving completely consistent IFMPRs is presented. Considering incomplete case, consistency-based models are built to determine missing values that can address incomplete IFMPRs with the ignored objects, namely, all information for them is unknown. After that, group decision-making with IFMPRs is studied. To measure the agreement degree between the DMs’ individual IFMPRs, a new consensus index is defined, and an interactive algorithm to improve the consensus is offered. Based on the consistency and consensus analysis, a new method to group decision-making with IFMPRs is developed. Finally, case studies are offered to show the application of the new procedure and to compare it with previous methods.