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