An approach to computing interval-valued discounted Shapley values for a class of cooperative games under interval data

Through adding a discounted factor, Shapley values of cooperative games are extended to interval-valued (IV) cooperative games. The main purpose of this paper is to propose the concept of IV discounted Shapley values and hereby develop a simplified method for computing IV discounted Shapley values for a class of IV cooperative games. In this method, we introduce the concept of discounted Shapley values of -cooperative games associated with IV cooperative games for any attitude factor alpha is an element of[0,1] and find a weaker coalition monotonicity-like condition so that the defined discounted Shapley values possess the monotonicity. Hence we can obtain the analytical formula of IV discounted Shapley value of any IV cooperative game with the coalition monotonicity-like through utilizing only the lower and upper bounds of coalitions' IV values. The proposed method utilizes the weaker coalition monotonicity-like condition rather than the irreversible interval subtraction and hereby can effectively overcome some irrational issues.