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The Multi-Attribute Group Decision-Making Method Based on Interval Grey Trapezoid Fuzzy Linguistic Variables.

Kedong Yin1,2, Pengyu Wang3, Xuemei Li4,5

  • 1School of Economics, Ocean University of China, Qingdao 266100, China. yinkedong@ouc.edu.cn.

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Summary

This study introduces improved grey relational methods for multi-attribute group decision-making (MAGDM) problems with unknown weights and interval grey trapezoid fuzzy linguistic variables (IGTFLVs). The proposed approach effectively determines expert and attribute weights for ranking alternatives.

Keywords:
grey relation analysisinterval grey trapezoid fuzzy linguistic variablesmulti-attribute group decision making

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Area of Science:

  • Operations Research
  • Decision Sciences
  • Artificial Intelligence

Background:

  • Multi-attribute group decision-making (MAGDM) presents challenges when attribute values are complex and weights are unknown.
  • Existing methods struggle with interval grey trapezoid fuzzy linguistic variables (IGTFLVs), a type of linguistic variable.
  • Accurate determination of expert and attribute weights is crucial for effective MAGDM.

Purpose of the Study:

  • To propose improved grey relational methods for MAGDM problems involving IGTFLVs with unknown weights.
  • To define novel concepts and operations for IGTFLVs, including their distance and projection.
  • To develop a framework for determining expert and attribute weights and ranking alternatives.

Main Methods:

  • Definition of interval grey trapezoid fuzzy linguistic variables (IGTFLVs), operational rules, distance, and projection formulas.
  • Determination of expert weights using the maximum proximity method based on IGTFLV projections.
  • Determination of attribute weights via the maximum deviation method and ranking of alternatives using improved grey relational analysis.

Main Results:

  • The study successfully defines key concepts and operations for IGTFLVs.
  • A novel method for determining expert and attribute weights in MAGDM is presented.
  • An illustrative example demonstrates the effectiveness and flexibility of the proposed IGTFLV-based approach.

Conclusions:

  • The proposed improved grey relational methods effectively address MAGDM problems with IGTFLVs and unknown weights.
  • The method provides a robust framework for determining weights and ranking alternatives.
  • The flexibility of IGTFLVs is highlighted, offering potential for broader applications in decision-making.