Comonotone aggregation operators

Abstract

We consider the aggregation operators which are comonotone-⊕-additive, i.e., ⊕-additive for comonotone functions; ⊕ is any pseudo-addition. The main result is a representation theorem which expresses any operator by means of a kind of general fuzzy integral. This expression uses a family of fuzzy measures linked by a ⊕- Cauchy equation. In particular, the family of fuzzy measures can be obtained from a “discriminant” fuzzy measure by a pseudo-multiplication. In this case, the aggregation operator is exactly expressed by a general fuzzy integral. The main result provides a large class of aggregation operators and gives a wide generalization of the well known characterization theorem of the Choquet’s integral.

Keywords

• aggregation operators
• comonotone additivity
• fuzzy integral
• cauchy’s equation