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

Discrete Integrals and Axiomatically Defined Functionals

1,*  and 2
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 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 which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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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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