Bi-cooperative games with fuzzy bi-coalitions

In this paper, we introduce the notion of a bi-cooperative game with fuzzy bi-coalitions and discuss the related properties. In real game theoretic decision making problems, many criteria concerning the formation of coalitions have bipolar motives. Our model tries to explore such bipolarity in fuzzy environment. The corresponding Shapley axioms are proposed. An explicit form of the Shapley value as a possible solution concept to a particular class of such games is also obtained. Our study is supplemented with an illustrative example.