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

Discrete Integrals and Axiomatically Defined Functionals

Erich Peter Klement 1,* email and Radko Mesiar 2 email
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; in revised form: 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.
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.

AMA Style

Klement EP, Mesiar R. Discrete Integrals and Axiomatically Defined Functionals. Axioms. 2012; 1(1):9-20.

Chicago/Turabian Style

Klement, Erich Peter; Mesiar, Radko. 2012. "Discrete Integrals and Axiomatically Defined Functionals." Axioms 1, no. 1: 9-20.

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