On Distances for Cooperative Games and Non-additive Measures with Communication Situations

Non-additive (fuzzy) measures also known as cooperative games or capacities are set functions that can be used to evaluate subsets of a reference set. In order to evaluate their similarities and differences, we can consider distances between pairs of measures. Games have been extended to communication situations in which besides of the game there is a graph that establishes which sets are feasible (which coalitions are possible, which individuals can cooperate). In this paper we consider the problem of defining a distance for pairs of measures when not all sets are feasible.