Choquet integrals with respect to fuzzy measure on fuzzy σ-algebra

Authors:
Yan Huang;Congxin Wu
Affiliations:
Harbin Institute of Technology, Harbin, P.R. China;Harbin Institute of Technology, Harbin, P.R. China
Venue:
ICMLC'05 Proceedings of the 4th international conference on Advances in Machine Learning and Cybernetics
Year:
2005

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Abstract

In this paper a new kind of Choquet integral with respect to fuzzy measure on fuzzy σ–algebra is introduced, and some elementary properties of this kind of Choquet integral are studied. Convergence theorems for sequences of Choquet integrals are shown. A transformation theorem is given, which reveals the relation between this kind of Choquet integral on fuzzy sets and the Choquet integral on classical crisp sets. Finally, a new set function defined by this kind of Choquet integral is discussed. This new set function preserves many structural characteristics of the original set function.