Interval Shapley value for fuzzy Cooperative Games

摘要

In this paper, we make a study of the Shapley value with characteristic functions from the viewpoint that the payoff of each coalition are often only imprecisely or ambiguously known to the players as an interval number. Axioms of Shapley value which was given by Shapley in 1953 have been extended for the Interval Shapley value. The explicit and exclusive Interval Shapley value has been put forward, which has been applied to profit allocation scheme among partners. Because of the interval payoffs, the results of imputation in this paper are also interval numbers. Moreover, it is proven that any crisp Shapley value that corresponds to a real number belonging to interval range is remain with the bound of Interval Shapley. Because Interval fuzzy number is special fuzzy number, the results of our paper lay the foundation for the research on the solution of cooperative games with other fuzzy forms of payoffs.