Payoff function of game coalition based on fuzzy chance constraint

This article researches the payoff of game coalition under fuzzy game environment. Fuzzy variables were allowed to describe the rates of players' participation to the fuzzy game coalition. A new concept of payoff function was proposed based on the fuzzy game concepts by Tsurumi. For the practical game problem that decision-makers will maximize the optimistic return or the pessimistic return at a predetermined confidence level, credibility measure of fuzzy variables were introduced. Moreover, a fuzzy chance-constrained programme model was built to seek the payoff of game coalition, which was the maximum optimistic return or pessimism return. The proposed model reflects that the payoff gained from fuzzy game coalition will more depend on player's preference.