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

Nian Zhang1, Yifan Zhou1, Qiang Pan1

  • 1School of Modern Posts, Chongqing University of Posts and Telecommunications, Chongqing 400065, China.

Mathematical Biosciences and Engineering : MBE
|January 19, 2023
PubMed
Summary

This study introduces a new triangular fuzzy method for multi-attribute decision-making, incorporating regret theory and catastrophe progression to improve investment decisions by accounting for decision-maker psychology and attribute importance.

Keywords:
catastrophe progressionmulti-attribute decision-makingregret theorytriangular fuzzy number

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Area of Science:

  • Decision Sciences
  • Fuzzy Logic
  • Operations Research

Background:

  • Traditional multi-attribute decision-making (MADM) methods often struggle with subjective weighting and decision-maker psychology.
  • Regret theory and catastrophe progression offer potential frameworks for addressing these limitations.

Purpose of the Study:

  • To develop a novel triangular fuzzy method for MADM.
  • To eliminate the influence of indicator weights on scheme selection.
  • To account for decision-makers' regret psychology.

Main Methods:

  • Utilized triangular fuzzy numbers to describe the decision matrix.
  • Constructed regret and rejoicing value matrices based on regret theory.
  • Employed the maximizing deviation method to improve attribute importance ranking.
  • Calculated comprehensive catastrophe progression attributes for alternative ranking.

Main Results:

  • The proposed method effectively eliminates the influence of indicator weights.
  • Decision-maker regret aversion and subjective weighting are successfully incorporated.
  • An investment project selection example demonstrated the method's availability and superiority.

Conclusions:

  • The novel method considers bounded rationality in decision-making.
  • Expands the application of catastrophe progression in a triangular fuzzy environment.
  • Offers a robust approach for complex MADM problems.