AN APPROACH TO COMPUTING INTERVAL-VALUED EGALITARIAN SHAPLEY VALUES OF INTERVAL-VALUED COOPERATIVE GAMES WITH COALITION MONOTONICITY-LIKE

There are not effective and practical methods for interval-valued (IV) cooperative games due to the invertible interval subtraction. This paper focuses on developing a fast and simplified approach to computing IV egalitarian Shapley values for such a rather large subclass of IV cooperative games. In this method, through adding some weaker coalition monotonicity-like conditions, it is proven that egalitarian Shapley value is monotonic and non-decreasing. Hence, the IV egalitarian Shapley value of IV cooperative games can be directly obtained by determining its lower and upper bounds, respectively. The method proposed in this paper does not use the Moore's interval subtraction and hereby can effectively avoid the issues resulted from it. Furthermore, some important properties of the IV egalitarian Shapley values of IV cooperative games are discussed. The feasibility and applicability of the method proposed in this paper are illustrated with real numerical examples.