A real Shapley value for evidential games with fuzzy characteristic function

Abstract

Game theory is a famous issue of expert decision making. The real Shapley value for cooperative games with fuzzy characteristic function has high performance in deal with cooperative games, which is an effective tool in deal with issues of game theory. The real Shapley value for cooperative games with fuzzy characteristic function is based on the level sets, which is the extent of fuzzy sets. However, the real Shapley value for cooperative games with fuzzy characteristic function cannot solve the evidential games problems. What is the real Shapley value for evidential games with fuzzy characteristic function is still an open problem. This paper proposes the real Shapley value for evidential games with characteristic function, which consists of level sets, the real evidential Shapley value, basic probability assignment function. The real Shapley value for evidential games with fuzzy characteristic function can solve the expert decision making issues under evidential environment, with the aid of basic probability assignment function. Meanwhile, the theorem of the proposed model has been discussed. Numerical examples has been applied to illustrate the effectiveness of the proposed model. The experimental results show that proposed model can obtain the real evidential Shapley value of a given evidential games and address the issues of expert decision making.