Choquet-Sugeno-like operator based on relation and conditional aggregation operators
| Autor: | Michał Boczek, Ondrej Hutník, Marek Kaluszka |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics Information Systems and Management Mathematics::Operator Algebras Measure (physics) Mathematics::General Topology Functional Analysis (math.FA) Computer Science Applications Theoretical Computer Science Copula (probability theory) Dependence relation Mathematics - Functional Analysis Mathematics::Logic Monotone polygon Operator (computer programming) Choquet integral Computer Science::Discrete Mathematics Artificial Intelligence Control and Systems Engineering Bounded function FOS: Mathematics Partition (number theory) Software Mathematics |
| Zdroj: | Information Sciences. 582:1-21 |
| ISSN: | 0020-0255 |
| DOI: | 10.1016/j.ins.2021.07.063 |
| Popis: | 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 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 C F 1 F 2 -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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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