Fuzzy-Set-Based Multi-Attribute Decision-Making, Its Computing Implementation, and Applications

The ordinal consistency of a fuzzy preference relation

Multi-attribute decision making (MADM) is a cognitive process for evaluating data with different attributes in order to select the optimal alternative from a finite number of alternatives. In the real world, a lot of MADM problems involve some random and ordinal variables. Therefore, in this paper, a MADM method based on stochastic data envelopment analysis (DEA) cross-efficiency with ordinal variable is proposed. First, we develop a stochastic DEA model with ordinal variable, which can derive self-efficiency and the optimal weight of each attribute for all decision making units (DMUs). To further improve its discrimination power, cross-efficiency as a significant extension is proposed, which utilizes peer DMUs’ optimal weight to evaluate the relative efficiency of each alternative. Then, based on self-efficiency and cross-efficiency of all DMUs, we construct corresponding fuzzy preference relations (FPRs) and consistent fuzzy preference relations (FPRs). In addition, we obtain the priority weight vector of all DMUs by utilizing the row wise summation technique according to the consistent FPRs. Finally, we provide a numerical example for evaluating operation performance of sustainable development of 15 listed banks in China, which illustrates the feasibility and applicability of the proposed MADM method based on stochastic DEA cross-efficiency with ordinal variable.

A fuzzy multi-criteria decision-making model by associating technique for order preference by similarity to ideal solution with relative preference relation

The breaking of additively reciprocal property of fuzzy preference relations and its implication to decision making under uncertainty

There are plenty of researches on group decision making (GDM) problem and most of them assume that all the experts are independent. However, the social network connection is an important characteristic among experts, and should been taken into account in the GDM decision process. The social network analysis (SNA) is a rapidly developing technology to deal with the problem about social network connections. In this paper, we address GDM problem with fuzzy preference relations where the experts have directed social network connections. And we use in-degree and out-degree centrality indices in SNA to build the social characteristics of the experts. Then we utilize the importance induced ordered weighted averaging(I-IOWA) operator to aggregate all the individual fuzzy preference relations with social indices. Furthermore,we investigate the reciprocity, additive consistency and acceptable consistency properties about the obtained group fuzzy preference relations. A procedure of addressing GDM problem with fuzzy preference relations where the experts are within directed social network connections is developed. Moreover, we compare the results of the case where all the experts are independent and the case where all the experts are within directed social network connections. Some useful tips that affect final outranking result in the directed graphical social network connection are obtained. In the end, we summarize the main results of this paper and point out some research directions for future research.

Fuzzy preference relations in models of decision making

On the basis of geometric consistency (GCI) of multiplicative preference relations and the transformation relation between multiplicative preference relations and fuzzy preference relation, inconsistency measure of fuzzy preference relation and the thresholds associated with it are studied. A new satisfactory consistency concept of fuzzy preference relation is defined. For a fuzzy preference relation, which does not possess satisfactory consistency, an improving consistency approach is provided. Then, programming models for estimating interval priority weights from fuzzy preference relations is established. Finally, an example is given to illustrate the validity and practicality of the proposed methods.

Considering the influence of undesirable outputs in environmental assessments of the practical production process, this paper proposes a DEA cross-efficiency method and fuzzy preference relation based on semi-disposability of undesirable outputs for environmental assessments, which combines self-evaluation with peer-evaluation and avoids potentially unrealistic weighting scheme. We first develop a new input-oriented DEA model based on semi-disposability of undesirable outputs. Then, the corresponding DEA cross-efficiency method is proposed to evaluate the homogeneous decision-making units (DMUs) and the additive fuzzy preference relation is constructed using the DEA cross-efficiency scores. An output-oriented DEA model is adopted to derive the priority vector from the constructed additive fuzzy preference relation. Furthermore, we summarize the specific procedures for environmental assessments based on DEA cross-efficiency and fuzzy preference relation. Finally, the practical example of industrial environment assessment of the Yangtze River Economic Belt is provided to show the applicability and effectiveness of the proposed method.

Group decision making with preference information on alternatives is an interesting and important research topic which has been receiving more and more attention in recent years. The purpose of this paper is to investigate multiple-attribute group decision-making (MAGDM) problems with distinct uncertain preference structures. We develop some linear-programming models for dealing with the MAGDM problems, where the information about attribute weights is incomplete, and the decision makers have their preferences on alternatives. The provided preference information can be represented in the following three distinct uncertain preference structures: 1) interval utility values; 2) interval fuzzy preference relations; and 3) interval multiplicative preference relations. We first establish some linear-programming models based on decision matrix and each of the distinct uncertain preference structures and, then, develop some linear-programming models to integrate all three structures of subjective uncertain preference information provided by the decision makers and the objective information depicted in the decision matrix. Furthermore, we propose a simple and straightforward approach in ranking and selecting the given alternatives. It is worth pointing out that the developed models can also be used to deal with the situations where the three distinct uncertain preference structures are reduced to the traditional ones, i.e., utility values, fuzzy preference relations, and multiplicative preference relations. Finally, we use a practical example to illustrate in detail the calculation process of the developed approach.

In this paper, we propose models to determine the weights of attributes by combining subjective information given by fuzzy preference relation and objective information given by the decision matrix. The fuzzy preference relations considered include the fuzzy preference relation with multiplicative transitivity and the fuzzy preference relation with additive transitivity. The proposed approaches are simpler than the previous methods that combine both subjective and objective information.

Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making

Some issues on consistency of fuzzy preference relations

A neural network approach to modeling fuzzy preference relations for multiple criteria decision making

On the equivalence of two optimization methods for fuzzy linear programming problems

In this paper, the multi-person decision making problems with various different types of incomplete linguistic preference relations are studied. Some new concepts, including incomplete uncertain linguistic preference relation, incomplete triangular fuzzy linguistic preference relation, incomplete trapezoid fuzzy linguistic preference relation, expected incomplete linguistic preference relation and acceptable expected incomplete linguistic preference relation, are defined. Based on some transformation functions, all these types of incomplete linguistic preference relations are transformed into the expected incomplete linguistic preference relations. By using the additive consistency property, the acceptable expected incomplete linguistic preference relations are then extended to the complete linguistic preference relations. Moreover, an approach is proposed for multi-person decision making based on multiple types of incomplete linguistic preference relations including incomplete traditional linguistic preference relations, incomplete uncertain linguistic preference relations, incomplete triangular fuzzy linguistic preference relations and incomplete trapezoid fuzzy additive linguistic preference relations.