The interaction and Möbius representations of fuzzy measures on finite spaces, k-additive measures: a survey

Abstract

This paper presents a synthesis of results on the concept of-additive measures and the notion of representation of a fuzzy measure, since their introduction by the author in 1996. The collection of results will limit itself to results which are not connected with multicriteria decision making, since those are presented in a companion paper in this book, co-authored with Marc Roubens. The paper presents the concept of representation of a set function over a finite set, and introduces the well-known Möbius representation, and the interaction representation. Properties and links among these representations are given, and the notion of-additive measure is introduced. 1

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