Title: Matrix games in intuitionistic fuzzy environment

Authors: Mijanur Rahaman Seikh; Prasun Kumar Nayak; Madhumangal Pal

Addresses: Department of Applied Mathematics, with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India ' Bankura Christian College, Bankura-722 101, India ' Department of Applied Mathematics, with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721 102, India

Abstract: This paper presents a new intuitionistic fuzzy optimisation (IFO) approach to solve matrix games under uncertainty. This approach is an application of the intuitionistic fuzzy set. First we have considered matrix game with intuitionistic fuzzy (IF) goals for each of a strategy in a payoff matrix in order to incorporate ambiguity of human judgements. The degree of membership is defined as the degree of satisfaction and the degree of nonmembership function have been taken for the degree of rejection. Then it converts the said problem into two conventional linear programming problems. Numerical example is provided to illustrate our approach.

Keywords: game theory; intuitionistic fuzzy sets; IFSs; intuitionistic fuzzy goals; intuitionistic fuzzy optimisation; IFO; fuzzy logic; matrix games; uncertainty; ambiguity; human judgement; linear programming.

DOI: 10.1504/IJMOR.2013.057491

International Journal of Mathematics in Operational Research, 2013 Vol.5 No.6, pp.693 - 708

Received: 29 Jun 2012
Accepted: 13 Aug 2012
Published online: 31 Mar 2014 *

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