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New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis.

Neeraj Gandotra1, Bartłomiej Kizielewicz2, Abhimanyu Anand1

  • 1Yogananda School of AI, Computers and Data Science, Shoolini University, Solan 173229, Himachal Pradesh, India.

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Summary

This study introduces a novel Pythagorean fuzzy entropy for Pythagorean fuzzy sets, enhancing information quantification in complex decision-making. The new measure proves reliable for assessing fuzziness in Pythagorean fuzzy sets and intuitionistic fuzzy sets.

Keywords:
COPRAS methodMCDAPythagorean fuzzy entropyPythagorean fuzzy setsentropy measuresmulti-criteria decision analysis

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Area of Science:

  • Fuzzy Set Theory
  • Information Theory
  • Decision Sciences

Background:

  • Intuitionistic fuzzy sets (IFS) have limitations in handling complex uncertain data.
  • Pythagorean fuzzy sets (PFS) extend IFS, offering improved capabilities to address imperfections.
  • Entropy measures quantify information content within fuzzy sets.

Purpose of the Study:

  • To propose a new Pythagorean fuzzy entropy measure for Pythagorean fuzzy sets.
  • To enhance the quantification of information within PFS.
  • To provide a flexible tool for complex multi-criteria decision-making problems with uncertain data.

Main Methods:

  • Development of a novel Pythagorean fuzzy entropy formula.
  • Application of the entropy measure in a multi-criteria company selection case study.
  • Comparative analysis with existing entropy measures for PFS and IFS.
  • Integration of the entropy measure into the Complex Proportional Assessment (COPRAS) method for weight calculation.

Main Results:

  • The proposed Pythagorean fuzzy entropy reliably quantifies the degree of fuzziness in both PFS and IFS.
  • Numerical illustrations demonstrate the effectiveness and flexibility of the new entropy measure.
  • The COPRAS method, utilizing weights derived from the proposed entropy, yields reliable decision-making outcomes.
  • Comparative analysis confirms the similarity of results with existing state-of-the-art entropy methods.

Conclusions:

  • The proposed Pythagorean fuzzy entropy is a valuable and flexible tool for complex decision-making under uncertainty.
  • The new entropy measure offers a reliable method for assessing information content in PFS and IFS.
  • The integration with COPRAS provides a robust approach for multi-criteria decision-making problems.