TitleTwofold integral: A Choquet integral and Sugeno integral generalization
Publication TypeMiscellaneous
Year of Publication2003
AuthorsTorra V
Abstract

Sugeno and Choquet integrals are well-known fuzzy integrals that are commonly in use for aggregation purposes. They integrate a function with respect to a fuzzy measure. Such fuzzy measure is used to represent some background knowledge about the information sources being aggregated. Murofushi and Sugeno defined in 1991 the fuzzy t-conorm integral, an integral that generalizes both Sugeno and Choquet integrals. Such generalization is based on the use of t-conorm and product-like operators that generalize addition/maximum and product/minimum present in the former integrals. In this way, fuzzy t-conorm integral corresponds to an integral of a function with respect to a single fuzzy measure. According to its construction, integral particularizations are achieved appropriately selecting t-conorm and t-norm like operators. In this work we introduce the {\em twofold integral}. This is an alternative operator that generalizes both Sugeno and Choquet integral. The approach is based on the use of two fuzzy measures instead of one. Particular selection of the fuzzy measures permits the reduction of the integral to either Sugeno or Choquet integrals. The motivation of our approach is to keep in a single operator the semantics of both measures.