Generalizations of k-order additive discrete fuzzy measures
Two types of generalizations of k-order additive discrete fuzzy measures recently introduced by Grabisch are shown. First, a special type of discrete fuzzy measures generalizing the pseudo-additive measures with respect to a Pan-addition + is introduced, following the ideas of Grabisch. A Mobius-like transformation of discrete fuzzy measures is presented and an evaluation formula for the corresponding Choquet-like integral is given, including the Sugeno integral. Next, k-order additive fuzzy measures on general spaces are introduced. Combination of both generalizations is discussed and several open problems are addressed. (C) 1999 Elsevier Science B.V. All rights reserved.
fuzzy measure measure pseudo-addition pseudo-additive measure sugeno integral choquet integral mobius transform