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

Abstract

We introduce a Choquet-Sugeno-like operator generalizing many operators for bounded functions and monotone measures from the literature, e.g., Sugeno-like operator, Lovász and Owen measure extensions, F-decomposition integral with respect to a partition decomposition system, and others. The new operator is based on the concepts of dependence relation and conditional aggregation operators, but it does not depend on t-level sets. We also provide conditions for which the Choquet-Sugeno-like operator coincides with some Choquet-like integrals defined on finite spaces and appeared recently in the literature, e.g. reverse Choquet integral, d-Choquet integral, F-based discrete Choquet-like integral, some version of C F 1 F 2 -integral, CC-integrals (or Choquet-like Copula-based integral) and discrete inclusion-exclusion integral. Some basic properties of the Choquet-Sugeno-like operator are studied.