A Study on Game Theory in Fuzzy Environment

Fuzzy set theory has a wide range of applications in operations research, war science, medical diagnosis, etc. The present monograph deals with the validity of applications of fuzzy set theory in matrix and bi-matrix games. The solution methodology of two-person matrix games with elements of pay-off matrix represented by triangular fuzzy numbers (TFNs) has been studied. Intuitionistic fuzziness in matrix/bi-matrix games can appear in many ways but three cases seem to be very natural. First one is that the goal may be intuitionistic fuzzy (I-fuzzy), second, that the elements of the pay-off matrix are I-fuzzy numbers and lastly the goals as well as the elements of the pay-off matrix are I-fuzzy. In this monograph the solution procedure of all such types of games have been investigated. A solution procedure for the matrix games where the elements of pay-off matrix are expressed by interval numbers has been explored. A number of practical implications have been incorporated to illustrate the methodologies.