Integrals based on monotone set functions

被引：55

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 50 条

[21] On the coincidence of measure-based decomposition and superdecomposition integrals
Li, Jun
Mesiar, Radko
Ouyang, Yao
FUZZY SETS AND SYSTEMS, 2023, 457 : 125 - 141
[22] SOME APPLICATIONS OF THE CHOQUET INTEGRAL WITH RESPECT TO A MONOTONE SET FUNCTION ON THE SET OF INTERVAL-VALUED NECESSITY MEASURES
Jang, Lee-Chae
JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2013, 15 (04) : 764 - 777
[23] Preference information modeling by empty interaction index based on monotone measure
Pap, Endre
Wu, Jianzhang
Szakal, Aniko
2015 16TH IEEE INTERNATIONAL SYMPOSIUM ON COMPUTATIONAL INTELLIGENCE AND INFORMATICS (CINTI), 2015, : 41 - 45
[24] A representation of a comonotone-additive and monotone functional by two Sugeno integrals
Pap, E
Mihailovic, B
FUZZY SETS AND SYSTEMS, 2005, 155 (01) : 77 - 88
[25] Sugeno integral of monotone functions based on Lebesgue measure
Ouyang, Yao
Fang, Jinxuan
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (02) : 367 - 374
[26] Copula-Based Universal Integrals
Klement, Erich Peter
Spizzichino, Fabio
Mesiar, Radko
Stupnanova, Andrea
2013 IEEE INTERNATIONAL CONFERENCE ON FUZZY SYSTEMS (FUZZ - IEEE 2013), 2013,
[27] Uniform and pointwise convergence of Bernstein-Durrmeyer operators with respect to monotone and submodular set functions
Gal, Sorin G.
Opris, Bogdan D.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 424 (02) : 1374 - 1379
[28] n-Monotone lower previsions and lower integrals
de Cooman, Gert
Troffaes, Matthias C. A.
Miranda, Enrique
ISIPTA 05-PROCEEDINGS OF THE FOURTH INTERNATIONAL SYMPOSIUM ON IMPRECISE PROBABILITIES AND THEIR APPLICATIONS, 2005, : 145 - 154
[29] A unified approach to the monotone convergence theorem for nonlinear integrals
Kawabe, Jun
FUZZY SETS AND SYSTEMS, 2016, 304 : 1 - 19
[30] Choquet integrals of fuzzifying measurable functions and their applications
Wood, J.
Kim, D.
Jang, L. C.
IRANIAN JOURNAL OF FUZZY SYSTEMS, 2023, 20 (05): : 151 - 164

← 1 2 3 4 5 →