Choquet-Sugeno-like operator based on relation and conditional aggregation operators

Abstract

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded nonnegative functions and monotone measures from the literature, e.g., the Sugeno-like operator, the Lovász and Owen measure extensions, the F-decomposition integral with respect to a partition decomposition system, and others. The new operator is based on concepts of dependence relation and conditional aggregation operators, but it does not depend on α-level sets. We also provide conditions under which the Choquet-Sugeno-like operator coincides with some Choquet-like integrals defined on finite spaces and appeared recently in the literature, e.g., the reverse Choquet integral, the d-Choquet integral, the F-based discrete Choquet-like integral, some version of the CF1F2-integral, the CC-integrals (or Choquet-like Copula-based integral) and the discrete inclusion-exclusion integral. Some basic properties of the Choquet-Sugeno-like operator are studied.