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

Abstract: We introduce a~\textit{Choquet-Sugeno-like operator} generalizing many operators for bounded functions and monotone measures from the literature, e.g., Sugeno-like operator, Lov\'{a}sz and Owen measure extensions, $\rF$-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, $\rF$-based discrete Choquet-like integral, some version of $C_{\rF_1\rF_2}$-integral, $\mathrm{C}\mathrm{C}$-integrals (or Choquet-like Copula-based integral) and discrete inclusion-exclusion integral. Some basic properties of the Choquet-Sugeno-like operator are studied.