Fubini-Like Theorem of Real-Valued Choquet Integrals for Set-Valued Mappings

被引：1

作者：

Zong, Gaofeng ^{[1
,2
]}

Chen, Zengjing ^{[2
,3
]}

Lan, Yuting ^{[3
]}

机构：

[1] Shandong Univ Finance & Econ, Sch Math & Quantitat Econ, Jinan, Peoples R China

[2] Shandong Univ Finance & Econ, Sch Math, Jinan, Peoples R China

[3] Shandong Univ Finance & Econ, Inst Financial Study, Jinan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS | 2016年 / 24卷 / 03期

基金：

美国国家科学基金会;

关键词：

Fubini-like theorem; Choquet integral; comonotonic; random set; set-valued mapping; NONADDITIVE MEASURE; LUSINS THEOREM; MEASURE-SPACES; EGOROFF THEOREM; CAPACITIES; PROBABILITIES; PRODUCTS;

D O I：

10.1142/S0218488516500197

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

The purpose of this paper is to establish a Fubini-like theorem of real-valued Choquet integrals for set-valued mappings in the frame of capacity theory. To this, we introduce the comonotonic random sets and slice-comonotonic set-valued mappings, which to make, good use of the comonotonic additivity of Choquet integrals.

引用

页码：387 / 403

页数：17

共 29 条

[21] Lusin's theorem on monotone measure spaces
Li, Jun
Mesiar, Radko
[J]. FUZZY SETS AND SYSTEMS, 2011, 175 (01) : 75 - 86
[22] Limit laws for non-additive probabilities and their frequentist interpretation
Marinacci, M
[J]. JOURNAL OF ECONOMIC THEORY, 1999, 84 (02) : 145 - 195
[23] Molchanov I., 2006, Theory of Random Sets
[24] Precupanu A., 2006, FUZZY SETS SYSTEMS, V204, P106
[25] A set-valued Egoroff type theorem
Precupanu, Anca
Gavrilut, Alina
[J]. FUZZY SETS AND SYSTEMS, 2011, 175 (01) : 87 - 95
[26] Products of capacities on separate spaces through additive measures
Skulj, D
[J]. FUZZY SETS AND SYSTEMS, 2005, 152 (02) : 289 - 301
[27] On Lusin's theorem for non-additive measures that take values in an ordered topological vector space
Watanabe, Toshikazu
Tanaka, Tamaki
[J]. FUZZY SETS AND SYSTEMS, 2014, 244 : 41 - 50
[28] On sufficient conditions for the Egoroff theorem of an ordered topological vector space-valued non-additive measure
Watanabe, Toshikazu
[J]. FUZZY SETS AND SYSTEMS, 2011, 162 (01) : 79 - 83
[29] On sufficient condition for the Egoroff theorem of an ordered vector space-valued non-additive measure
Watanabe, Toshikazu
[J]. FUZZY SETS AND SYSTEMS, 2010, 161 (22) : 2919 - 2922

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