On the axiomatization of some classes of discrete universal integrals

Authors:
Erich Peter Klement;Radko Mesiar
Affiliations:
Department of Knowledge-Based Mathematical Systems, Johannes Kepler University, Linz, Austria;Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Bratislava, Slovakia and Institute of Theory of Information and Automation, Czech ...
Venue:
Knowledge-Based Systems
Year:
2012

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Abstract

Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255-261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001) 164-172], we provide a general axiomatization of some classes of discrete universal integrals, including the case of discrete copula-based universal integrals (as usual, the product copula corresponds just to the Choquet integral, and the minimum to the Sugeno integral).