Interaction transform of set functions over a finite set

The paper introduces a new transform of set functions over a finite set, wh ich is linear and invertible as the well-known Mobius transform in combinat orics. This transform leads to the interaction index, a central concept in multicriteria decision making. The interaction index of a singleton happens to be the Shapley value of the set function or, in terms of cooperative ga me theory, of the value function of the game. Properties of this new transf orm are studied in detail, and some illustrative examples are given. (C) 19 99 Elsevier Science Inc. All rights reserved.