COALITIONAL GAME WITH FUZZY PAYOFFS AND CREDIBILISTIC SHAPLEY VALUE

Abstract

Coalitional game deals with situations that involve cooperations among players, and there are different solution concepts such as the core,<br />the Shapley value and the kernel. In many situations, there is no way to predict the payoff functions except for the expert experiences<br />and subjective intuitions, which leads to the coalitional game with fuzzy payoffs. Within the framework of credibility theory, this paper employs<br />two credibilistic approaches to define the behaviors of players under fuzzy situations. Correspondingly, two variations of Shapley value are<br />proposed as the solutions of the coalitional game with fuzzy payoffs. Meanwhile, some characterizations of the credibilistic Shapley value<br />are investigated. Finally, an example is provided for illustrating the usefulness of the theory developed in this paper.