Integrals based on monotone set functions

被引：56

作者：

Klement, Erich Peter ^{[1
,2
]}

Li, Jun ^{[3
]}

Mesiar, Radko ^{[4
,5
]}

Pap, Endre ^{[6
,7
]}

机构：

[1] Johannes Kepler Univ Linz, A-4040 Linz, Austria

[2] JKU Softwarepk Hagenberg, A-4232 Hagenberg, Austria

[3] Commun Univ China, Sch Sci, Beijing 100024, Peoples R China

[4] Slovak Univ Technol Bratislava, Fac Civil Engn, Bratislava 81368, Slovakia

[5] Univ Ostrava, CZ-70103 Ostrava, Czech Republic

[6] Singidunum Univ, Belgrade 11000, Serbia

[7] Obuda Univ, H-1034 Budapest, Hungary

来源：

FUZZY SETS AND SYSTEMS | 2015年 / 281卷

基金：

中国国家自然科学基金;

关键词：

Monotone measure; Choquet integral; Shilkret integral; Sugeno integral; Universal integral; Decomposition integral; CHEBYSHEV TYPE INEQUALITIES; FUZZY MEASURES; CHOQUET; SUGENO; DISTRIBUTIVITY; MULTIPLICATION; CONVERGENCE; PROBABILITY;

D O I：

10.1016/j.fss.2015.07.010

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

An overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set (called here monotone measures). Our survey includes not onlythe Choquet integral (1954) [10], the Shilkret integral (1971) [66] and the Sugeno integral (1974) [71] and some of their properties, but also some more general and more recent concepts as universal integrals Klement etal. (2010) [27] and decomposition integrals Even (2014) [13], together with some of their properties, such as integral inequalities and convergence theorems. (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：88 / 102

页数：15

共 76 条

[1] On Stolarsky inequality for Sugeno and Choquet integrals [J].