Authors: Mijanur Rahaman Seikh; Prasun Kumar Nayak; Madhumangal Pal
Addresses: Department of Mathematics, Kazi Nazrul University, Asansol-713 303, India ' Department of Mathematics, Midnapore College, Midnapore-721 101, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Mindapore-721 102, India
Abstract: This paper presents a new solution methodology for solving bi-matrix games with intuitionistic fuzzy (IF) goals for each of the strategy in pay-off matrices. The solution procedure for bi-matrix games with IF goals have been studied by Nayak and Pal (2010) by defining the concept of a Nash equilibrium solution by means of degree of attainment. In Nayak and Pal's (2010) approach the result of crisp bi-matrix games do not seem to follow from the formulation of IF bi-matrix games. In this paper, the solution methodology for such games is conceptualised by introducing aspiration level approach and it is shown that the formulation of IF bi-matrix game reduces to the formulation of crisp bi-matrix game under certain conditions. Also in our proposed methodology it is ensured that the bi-matrix games with IF goals is an extension of the bi-matrix games with fuzzy goals which is not the case in Nayak and Pal's (2010) approach. Numerical example is provided to illustrate our approach.
Keywords: mathematical programming; game theory; bi-matrix games; intuitionistic fuzzy goals; intuitionistic fuzzy optimisation; IFO.
International Journal of Fuzzy Computation and Modelling, 2015 Vol.1 No.4, pp.362 - 381
Received: 25 Oct 2014
Accepted: 18 Apr 2015
Published online: 30 Apr 2016 *