Generalizations of k-order additive discrete fuzzy measures

Abstract 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.

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