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Innovative intuitionistic fuzzy fairly aggregation operators with linear programming based decision-making approach.

Muhammad Riaz1, Hafiz Muhammad Athar Farid1, Rukhsana Kausar1

  • 1Department of Mathematics, University of the Punjab, Lahore, Pakistan.

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Summary
This summary is machine-generated.

This study introduces new operational rules and aggregation operators for intuitionistic fuzzy sets (InFS) to improve decision-making with incomplete information. The developed methods offer fair solutions for multi-criteria decision-making (MCDM) problems.

Keywords:
Fairly aggregation operatorsIntuitionistic fuzzy setLinear programming modelMCDM

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Area of Science:

  • Decision Sciences
  • Fuzzy Logic Systems
  • Operations Research

Background:

  • Intuitionistic fuzzy set (InFS) theory offers a robust framework for strategic planning and decision-making, particularly when dealing with uncertainty.
  • Aggregation operators (AOs) are crucial for synthesizing information in decision processes, but challenges arise with incomplete data.
  • Existing methods struggle to provide fair and neutral solutions in complex decision environments with limited information.

Purpose of the Study:

  • To develop novel operational rules and aggregation operators within the intuitionistic fuzzy set environment.
  • To introduce a fair approach for handling intuitionistic fuzzy information, utilizing proportional distribution.
  • To construct a fair multi-criteria decision-making (MCDM) method using the proposed operators and addressing partial weight information.

Main Methods:

  • Development of new operational laws for InFS based on proportional distribution.
  • Construction of fair aggregation operators for intuitionistic fuzzy numbers.
  • Integration of a linear programming model to determine criteria weights with partial information.
  • Formulation of a fair MCDM method incorporating multiple decision-makers' evaluations.

Main Results:

  • Novel operational rules and fair aggregation operators for InFS were successfully established.
  • A fair MCDM method was constructed, demonstrating efficacy in handling incomplete information and partial weights.
  • The proposed method provides a neutral or fair remedy for decision-making challenges in InFS environments.
  • A rigorous implementation validated the effectiveness of the developed aggregation operators.

Conclusions:

  • The proposed operational rules and aggregation operators enhance decision-making capabilities within the intuitionistic fuzzy set framework.
  • The developed fair MCDM method effectively addresses challenges posed by incomplete information and partial weight data.
  • This research contributes innovative tools for strategic planning and complex decision analysis under uncertainty.