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A novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance with incomplete weight information

Xiaoyue Liu (School of Information Technology and Management, University of International Business and Economics, Beijing, China)
Xiaolu Wang (School of Economics and Management, Shanxi University, Taiyuan, China)
Li Zhang (School of Information Technology and Management, University of International Business and Economics, Beijing, China)
Qinghua Zeng (School of Investigation and Counterterrorism, People’s Public Security University of China, Beijing, China)

Kybernetes

ISSN: 0368-492X

Article publication date: 8 July 2019

Issue publication date: 23 September 2019

101

Abstract

Purpose

With respect to multiple attribute group decision-making (MAGDM) in which the assessment values of alternatives are denoted by normal discrete fuzzy variables (NDFVs) and the weight information of attributes is incompletely known, this paper aims to develop a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and then applies the proposed method for selecting the most desirable investment alternative under uncertain environment.

Design/methodology/approach

First, by aggregating the membership degrees of an alternative to a scale provided by all decision-makers into a triangular fuzzy number, the credibility degree and expect the value of a triangular fuzzy number are calculated to construct the group fuzzy stochastic decision matrix. Second, based on determining the credibility distribution functions of NDFVs, the fuzzy stochastic dominance relations between alternatives on each attribute are obtained and the fuzzy stochastic dominance degree matrices are constructed by calculating the dominance degrees that one alternative dominates another on each attribute. Subsequently, calculating the overall fuzzy stochastic dominance degrees of an alternative on each attribute, a single objective non-linear optimization model is established to determine the weights of attributes by maximizing the relative closeness coefficients of all alternatives to positive ideal solution. If the information about attribute weights is completely unknown, the idea of maximizing deviation is used to determine the weights of attributes. Finally, the ranking order of alternatives is determined according to the descending order of corresponding relative closeness coefficients and the best alternative is determined.

Findings

This paper proposes a novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance, and a case study of investment alternative selection problem is provided to illustrate the applicability and sensitivity of the proposed method and its effectiveness is demonstrated by comparison analysis with the proposed method with the existing fuzzy stochastic MAGDM method. The result shows that the proposed method is useful to solve the MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known.

Originality/value

The contributions of this paper are that to describe the dominance relations between fuzzy variables reasonably and quantitatively, the fuzzy stochastic dominance relations between any two fuzzy variables are redefined and the concept of fuzzy stochastic dominance degree is proposed to measure the dominance degree that one fuzzy variable dominate another; Based on credibility theory and fuzzy stochastic dominance, a novel fuzzy stochastic MAGDM method is proposed to solve MAGDM problems in which the assessment values of alternatives are denoted by NDFVs and the weight information of attributes is incompletely known. The proposed method has a clear logic, which not only can enrich and develop the theories and methods of MAGDM but also provides decision-makers a novel method for solving fuzzy stochastic MAGDM problems.

Keywords

Acknowledgements

Funding: Supported by “the Fundamental Research Funds for the Central Universities” in UIBE (CXTD10-06).

Citation

Liu, X., Wang, X., Zhang, L. and Zeng, Q. (2019), "A novel fuzzy stochastic MAGDM method based on credibility theory and fuzzy stochastic dominance with incomplete weight information", Kybernetes, Vol. 48 No. 9, pp. 2030-2064. https://doi.org/10.1108/K-08-2018-0438

Publisher

:

Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited

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