Multi-attribute decision-making method with triangular fuzzy numbers based on regret theory and the catastrophe progression method

Nian Zhang; Yifan Zhou; Qiang Pan; Guiwu Wei; Nian Zhang; Yifan Zhou; Qiang Pan; Guiwu Wei

doi:10.3934/mbe.2022559

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 12: 12013-12030. doi: 10.3934/mbe.2022559

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Multi-attribute decision-making method with triangular fuzzy numbers based on regret theory and the catastrophe progression method

1.
School of Modern Posts, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2.
School of Business, Sichuan Normal University, Chengdu 610101, China
Academic editor: Sheldon Wang

Received: 25 May 2022 Revised: 12 July 2022 Accepted: 14 July 2022 Published: 18 August 2022

The purpose of this paper was to develop a novel triangular fuzzy method for multi-attribute decision-making to eliminate the influence of indicator weights on scheme selection and account for the regret psychology of decision-makers. Therefore, considering the consequences of regret aversion and subjective weighting, we propose a multi-attribute decision-making method with triangular fuzzy number based on regret theory and catastrophe progression. First, to eliminate the influence of various dimensions on the decision-making results, the decision matrix is described by a triangular fuzzy number, and the regret value matrix and rejoicing value matrix are independently constructed by applying regret theory. Second, the importance ranking of attributes is improved to eliminate the influence of subjective weighting by employing the maximizing deviation method; and the comprehensive catastrophe progression attribute is calculated to rank the alternatives. Finally, an instance of investment project selection is provided to prove the availability and superiority. In conclusion, the proposed method not only considers decision-makers' bounded rationality for decision-making, but it also expands the application of catastrophe progression methods under the condition of a triangular fuzzy environment.
- regret theory,
- catastrophe progression,
- triangular fuzzy number,
- multi-attribute decision-making
Citation: Nian Zhang, Yifan Zhou, Qiang Pan, Guiwu Wei. Multi-attribute decision-making method with triangular fuzzy numbers based on regret theory and the catastrophe progression method[J]. Mathematical Biosciences and Engineering, 2022, 19(12): 12013-12030. doi: 10.3934/mbe.2022559

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Abstract

The purpose of this paper was to develop a novel triangular fuzzy method for multi-attribute decision-making to eliminate the influence of indicator weights on scheme selection and account for the regret psychology of decision-makers. Therefore, considering the consequences of regret aversion and subjective weighting, we propose a multi-attribute decision-making method with triangular fuzzy number based on regret theory and catastrophe progression. First, to eliminate the influence of various dimensions on the decision-making results, the decision matrix is described by a triangular fuzzy number, and the regret value matrix and rejoicing value matrix are independently constructed by applying regret theory. Second, the importance ranking of attributes is improved to eliminate the influence of subjective weighting by employing the maximizing deviation method; and the comprehensive catastrophe progression attribute is calculated to rank the alternatives. Finally, an instance of investment project selection is provided to prove the availability and superiority. In conclusion, the proposed method not only considers decision-makers' bounded rationality for decision-making, but it also expands the application of catastrophe progression methods under the condition of a triangular fuzzy environment.

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