On the axiomatization of some classes of discrete universal integrals

Erich Klement; Radko Mesiar

doi:10.1016/j.knosys.2011.10.015

On the axiomatization of some classes of discrete universal integrals

Erich Klement, Radko Mesiar

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Pages (from-to)	13-18
Number of pages	6
Journal	Knowledge-Based Systems
Volume	28
DOIs	https://doi.org/10.1016/j.knosys.2011.10.015
Publication status	Published - 2012

Fields of science

101001 Algebra
101 Mathematics
102 Computer Sciences
101013 Mathematical logic
101020 Technical mathematics
102001 Artificial intelligence
102003 Image processing
202027 Mechatronics
101019 Stochastics
211913 Quality assurance

JKU Focus areas

Computation in Informatics and Mathematics
Mechatronics and Information Processing
Nano-, Bio- and Polymer-Systems: From Structure to Function

Access to Document

10.1016/j.knosys.2011.10.015

Cite this

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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).",

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AU - Mesiar, Radko

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U2 - 10.1016/j.knosys.2011.10.015

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