Modeling interaction phenomena using fuzzy measures: on the notions of interaction and independence

Interaction phenomena among elements of a finite set can be modeled by a discrete fuzzy measure. The notion of marginal interaction between two elements is at the root of the definition of interaction. We first extend this notion by defining that of marginal interaction among pairwise disjoint subsets and we study some of its properties. Then, we generalize the notion of interaction index to pairwise disjoint subsets. Finally, we formalize the intuitive notion of independence and we propose the concept of measure of marginal amount of interaction in order to "fill the gap" between the notions of interaction and independence. (C) 2002 Elsevier Science B.V. All rights reserved.