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Discrete Integrals and Axiomatically Defined Functionals
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Altenbergerstraße 69, Linz, Austria
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, Bratislava, Slovakia
* Author to whom correspondence should be addressed.
Received: 5 March 2012; in revised form: 13 April 2012 / Accepted: 13 April 2012 / Published: 20 April 2012
Abstract: Several discrete universal integrals on finite universes are discussed from an axiomatic point of view. We start from the first attempt due to B. Riemann and cover also most recent approaches based on level dependent capacities. Our survey includes, among others, the Choquet and the Sugeno integral and general copula-based integrals.
Keywords: capacity; Choquet integral; copula; fuzzy integral; OWA operator; OMA operator; Sugeno integral
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MDPI and ACS Style
Klement, E.P.; Mesiar, R. Discrete Integrals and Axiomatically Defined Functionals. Axioms 2012, 1, 9-20.
Klement EP, Mesiar R. Discrete Integrals and Axiomatically Defined Functionals. Axioms. 2012; 1(1):9-20.
Klement, Erich Peter; Mesiar, Radko. 2012. "Discrete Integrals and Axiomatically Defined Functionals." Axioms 1, no. 1: 9-20.