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Axioms 2012, 1(1), 9-20; doi:10.3390/axioms1010009

Discrete Integrals and Axiomatically Defined Functionals

1
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Altenbergerstraße 69, Linz, Austria
2
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 / Revised: 13 April 2012 / Accepted: 13 April 2012 / Published: 20 April 2012
(This article belongs to the Special Issue Axioms: Feature Papers)
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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. View Full-Text
Keywords: capacity; Choquet integral; copula; fuzzy integral; OWA operator; OMA operator; Sugeno integral capacity; Choquet integral; copula; fuzzy integral; OWA operator; OMA operator; Sugeno integral
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Klement, E.P.; Mesiar, R. Discrete Integrals and Axiomatically Defined Functionals. Axioms 2012, 1, 9-20.

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