Some Algorithms to Determine Value of Game in Fuzzy Environment

Abstract

The fuzzy set theory has been applied in almost every business enterprise as well as in everyday life. Ranking function is an important technique that is used for ordering of different fuzzy numbers by converting the each fuzzy number into a single value. In the study, and#945; cut ranking approach and incentre of centroids approach has been applied to the pentagonal, hexagonal, heptagonal and octagonal fuzzy numbers to convert them into crisp numbers. Later on different game problems with payoffs expressed in these fuzzy numbers have been considered and solved by converting them into crisp game problems using the two ranking techniques. newlineIntuitionistic fuzzy sets, as a generalization of Zadeh fuzzy sets, can better express and deal with uncertainty by introducing hesitation. This study has proposed the use of centroid method to rank the trapezoidal intuitionistic fuzzy numbers and further provides a solution methodology for fuzzy matrix games with payoffs expressed in trapezoidal intuitionistic fuzzy numbers. newlineIn the real world competitive situations, it is really worthwhile to consider the evaluation by group of experts rather than a single expert. The existing game models cannot solve the matrix game problem when the expected payoffs according to the opinion of more than one expert have been considered. In the present study, aggregation operators have been used to combine the payoffs given by different experts and then solved the intuitionistic fuzzy matrix game based on the aggregated opinion of more than one expert. A new method has been proposed to solve the fuzzy games in which the payoffs have been expressed in intuitionistic fuzzy numbers by using linear and non linear programming models. newlineBi matrix game theory is very important tool in the situation when the players are not antagonistic. A solution procedure has been designed to solve the fuzzy bi matrix game problem with the collective payoff matrices newline newline