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.
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页码：683 / 688
页数：6
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