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

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 Lovasz 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 a-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 C-F1F2-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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This study introduces a generalized Choquet-Sugeno-like operator that can extend many existing operators for bounded nonnegative functions and monotone measures. The new operator is based on concepts of dependence relation and conditional aggregation operators, while not depending on a-level sets. Conditions under which the Choquet-Sugeno-like operator coincides with some Choquet-like integrals on finite spaces have been provided, and some basic properties of the operator have been studied.