Real-valued Choquet integrals for set-valued mappings

Yan Huang; Congxin Wu

doi:10.1016/j.ijar.2013.09.011

Real-valued Choquet integrals for set-valued mappings

Yan Huang^*
, Congxin Wu

^*Corresponding author for this work

School of Materials Science and Engineering

Harbin Institute of Technology

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

8 Scopus citations

Abstract

In this paper a new kind of real-valued Choquet integrals for set-valued mappings is introduced, and some elementary properties of this kind of Choquet integrals are studied. Convergence theorems of a sequence of Choquet integrals for set-valued mappings are shown. However, in the case of the monotone convergence theorem of the nonincreasing sequence of Choquet integrals for set-valued mappings, we point out that the integrands must be closed. Specially, this kind of real-valued Choquet integrals for set-valued mappings can be regarded as the Choquet integrals for single-valued functions.

Original language	English
Pages (from-to)	683-688
Number of pages	6
Journal	International Journal of Approximate Reasoning
Volume	55
Issue number	2
DOIs	https://doi.org/10.1016/j.ijar.2013.09.011
State	Published - Jan 2014

Keywords

Choquet integral
Fuzzy measure
Monotone convergence
Set-valued mapping

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10.1016/j.ijar.2013.09.011

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AB - In this paper a new kind of real-valued Choquet integrals for set-valued mappings is introduced, and some elementary properties of this kind of Choquet integrals are studied. Convergence theorems of a sequence of Choquet integrals for set-valued mappings are shown. However, in the case of the monotone convergence theorem of the nonincreasing sequence of Choquet integrals for set-valued mappings, we point out that the integrands must be closed. Specially, this kind of real-valued Choquet integrals for set-valued mappings can be regarded as the Choquet integrals for single-valued functions.

KW - Choquet integral

KW - Fuzzy measure

KW - Monotone convergence

KW - Set-valued mapping

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ER -

Real-valued Choquet integrals for set-valued mappings

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