Linear non-additive set-functions

Bernadette Bouchon-Meunier (1) , Radko Mesiar , Dan A. Ralescu

1 MALIRE - Machine Learning and Information Retrieval

It is known that for basic linear fuzzy measures the Aumann and the Choquet integrals defined on a special class of fuzzy subsets of some Banach space commute. We characterize basic linear fuzzy measures by means of appropriate linear functionals, and consequently the relevant integral representation (by means of the Lebesgue integral) is introduced. As a corollary the well-known additivity of perimeters of convex subsets in the real plane is obtained.

Domaines: Informatique [cs]

Bernadette Bouchon-Meunier, Radko Mesiar, Dan A. Ralescu. Linear non-additive set-functions. International Journal of General Systems, 2004, 33 (1), pp.89-98. ⟨10.1080/0308107032000141064⟩. ⟨hal-01171015⟩