Real-valued Choquet integrals for set-valued mappings

被引：8

作者：

Huang, Yan ^{[1
]}

Wu, Congxin ^{[1
]}

机构：

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2014年 / 55卷 / 02期

关键词：

Fuzzy measure; Set-valued mapping; Choquet integral; Monotone convergence; FUZZY MEASURES; NULL SETS;

D O I：

10.1016/j.ijar.2013.09.011

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：683 / 688

页数：6

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