Pythagorean Fuzzy Approach to Game Theory

Anju Thomas; Shiny Jose

doi:10.17485/IJST/v16iSP4.ICAMS131

Article

Pythagorean Fuzzy Approach to Game Theory

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16iSP4.ICAMS131

Year: 2023, Volume: 16, Issue: Special Issue 4, Pages: 22-28

Original Article

Pythagorean Fuzzy Approach to Game Theory

Anju Thomas^1*, Shiny Jose²

¹Department of Mathematics, St. Thomas College, Palai, Kerala, India
²Associate Professor in Mathematics, St. George’s College Aruvithura, Kerala, India

*Corresponding Author
Email: [email protected]

Received Date:12 October 2023, Accepted Date:22 November 2023, Published Date:25 December 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objectives: To study and tackle the impreciseness, vagueness and hesitancy involved in one of the decision-making problems say matrix games. This paper has done it using the most apt and innovative tool, Pythagorean Fuzzy sets. The objective of the paper is to define the Mathematical model of Pythagorean Fuzzy Matrix Game, study its properties and develop an innovative algorithm to solve it. These innovative concepts are made lucid through numerical illustrations. Methods: The matrix games solved using Fuzzy optimization tools and Intuitionistic fuzzy optimization techniques are analyzed. We came to the conclusion that the hesitancy associated with choosing strategies for players and payoff are not fully considered. Hence the strategy Pythagorean fuzzy optimization tool is used. The data set considered in this study are collected from a faculty of Physical Education Department in a college. Using the innovative algorithm and data set collected the study is completed. Findings: The Pythagorean fuzzy Expected Payoff function and a new ranking function for Pythagorean fuzzy number is found out in this paper. Moreover, the notion of Pythagorean Fuzzy Saddle point is also proposed in this paper. Then we have introduced a novel algorithm called Pythagorean Minimax Dominian Algorithm to solve Pythagorean fuzzy game problem and it is illustrated through two numerical examples involving two situations. Novelty: This study explored concepts of game theory under Pythagorean fuzzy environment. The outlined mathematical model of Pythagorean fuzzy matrix game and the algorithm to solve it is novel in the research field.

Keywords: Pythagorean fuzzy set, Pythagorean fuzzy Number, Pythagorean fuzzy Matrix Game, Pythagorean fuzzy saddle point, Pythagorean fuzzy Expected payoff function

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Copyright

© 2023 Thomas & Jose. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)