Integrals Based on Monotone Measure: Optimization Tools and Special Functionals

Abstract : Integrals on finite spaces (e.g., sets of criteria in multicriteria decision support) based on capacities are discussed, axiomatized and examplified. We introduce first the universal integrals, covering the Choquet, Shilkret and Sugeno integrals. Based on optimization approach, we discuss decomposition and superdecomposition integrals. We introduce integrals which are universal and decomposition (superdecomposition) ones and integrals constructed by means of copulas. Several distinguished integrals are represented as particular functionals. Finally, we recall also OWA operators and some their generalizations.
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Radko Mesiar. Integrals Based on Monotone Measure: Optimization Tools and Special Functionals. 14th Computer Information Systems and Industrial Management (CISIM), Sep 2015, Warsaw, Poland. pp.48-57, ⟨10.1007/978-3-319-24369-6_4⟩. ⟨hal-01444500⟩

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