Two new characterizations of universal integrals on the scale [0, 1]

Salvatore Greco; Radko Mesiar; Fabio Rindone

doi:10.1016/j.ins.2013.12.056

Two new characterizations of universal integrals on the scale [0, 1]

Salvatore Greco, Radko Mesiar, Fabio Rindone

Centre of Operational Research and Decision Analysis

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Abstract

The concept of universal integral, recently proposed and axiomatized, encompasses several integrals, including the Choquet, Shilkret and Sugeno integrals. In this paper we present two new axiomatizations of universal integrals on the scale [0,1]. In the first characterization, we look at universal integrals on the scale [0,1] as families of aggregation functions F satisfying some desired properties. The second characterization is given in the framing in which the original definition of universal integral was provided.

Original language	English
Pages (from-to)	217-224
Journal	Information Sciences
Volume	267
Early online date	16 Jan 2014
DOIs	https://doi.org/10.1016/j.ins.2013.12.056
Publication status	Published - 20 May 2014

Keywords

Aggregation functions
universal integrals
non-additive integrals
fuzzy measure

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10.1016/j.ins.2013.12.056

GRECO_2014_cright_IS_Two_new_characterizations_of_universal_integrals_on_the_scale
NOTICE: this is the author’s version of a work that was accepted for publication in 'Information sciences'. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in 'Information sciences', [VOL: 267, 20/05/2014] DOI: 10.1016/j.ins.2013.12.056
Accepted author manuscript (Post-print), 119 KBLicence: CC BY-NC-ND

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title = "Two new characterizations of universal integrals on the scale [0, 1]",

abstract = "The concept of universal integral, recently proposed and axiomatized, encompasses several integrals, including the Choquet, Shilkret and Sugeno integrals. In this paper we present two new axiomatizations of universal integrals on the scale [0,1]. In the first characterization, we look at universal integrals on the scale [0,1] as families of aggregation functions F satisfying some desired properties. The second characterization is given in the framing in which the original definition of universal integral was provided.",

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N1 - Accepted - 30/12/2013 NOTICE: this is the author’s version of a work that was accepted for publication in 'Information sciences'. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in 'Information sciences', [VOL: 267, 20/05/2014] DOI: 10.1016/j.ins.2013.12.056

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KW - non-additive integrals

KW - fuzzy measure

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Two new characterizations of universal integrals on the scale [0, 1]

Abstract

Keywords

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