Solving Bi-matrix Games with Pay-offs of Triangular In-tuitionistic Fuzzy Numbers

Authors

  • Mijanur Rahaman Seikh Department of Mathematics Kazi Nazrul University, Asansole-713304
  • Prasun Kumar Nayak Bankura Christian College Bankura, India
  • Madhumangal Pal Department of Mathematics, Vidyasagar University

Abstract

This paper presents a solution methodology for bi-matrix games in which pay-off ma-trices are represented by triangular intuitionistic fuzzy numbers (TIFNs). In this methodology, a new ranking function is defined to defuzzify the TIFNs. A non-linear intuitionistic fuzzy (I-fuzzy) programming problem is constructed to conceptualize the term equilibrium solution for such type
of bi-matrix games. It is shown that this non-linear I-fuzzy programming problem is a generaliza-tion of fuzzy non-linear programming problem. Finally, based on the ranking function the problem is transformed into a crisp non-linear programming problem which can be solved to obtain the
equilibrium solution for each player. Numerical simulation is provided to show the validity and applicability of this methodology.

Downloads

Published

2015-04-30

Issue

Vol. 8 No. 2: (April 2015)

Section

Game Theory

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

Solving Bi-matrix Games with Pay-offs of Triangular In-tuitionistic Fuzzy Numbers. (2015). European Journal of Pure and Applied Mathematics, 8(2), 153-171. https://www.ejpam.com/index.php/ejpam/article/view/2332