THE CHOQUET INTEGRAL AS LEBESGUE INTEGRAL AND RELATED INEQUALITIES

被引：0

作者：

Mesiar, Radko ^{[1
]}

Li, Jun ^{[2
]}

Pap, Endre ^{[3
]}

机构：

[1] Slovak Tech Univ Bratislava, Dept Math & Descript Geometry, Fac Civil Engn, Bratislava 81368, Slovakia

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

[3] Univ Novi Sad, Dept Math & Informat, Novi Sad 21000, Serbia

来源：

KYBERNETIKA | 2010年 / 46卷 / 06期

关键词：

Choquet integral; comonotone functions; integral inequalities; monotone measure; modularity; FUZZY INTEGRALS; ADDITIVITY;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Holder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered functions is shown to be a sufficient constraint ensuring the validity of all discussed inequalities for the Choquet integral, independently of the underlying monotone measure.

引用

页码：1098 / 1107

页数：10

共 16 条

[1] [Anonymous], 2009, GEN MEASURE THEORY
[2] BENVENUTI P, 2002, HDB MEASURE THEORY, V2, P1329
[3] Choquet G., 1954, Ann. Institute. Fourier (Grenoble), V5, P131, DOI DOI 10.5802/AIF.53
[4] Denneberg D., 1994, NONADDITIVE MEASURE
[5] A Chebyshev type inequality for fuzzy integrals
Flores-Franulic, A.
Roman-Flores, H.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2007, 190 (02) : 1178 - 1184
[6] A Universal Integral as Common Frame for Choquet and Sugeno Integral
Klement, Erich Peter
Mesiar, Radko
Pap, Endre
[J]. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2010, 18 (01) : 178 - 187
[7] General Chebyshev type inequalities for Sugeno integrals
Mesiar, Radko
Ouyang, Yao
[J]. FUZZY SETS AND SYSTEMS, 2009, 160 (01) : 58 - 64
[8] NARUKAWA Y, 2007, P IEEE INT C FUZZ SY
[9] An inequality related to Minkowski type for Sugeno integrals
Ouyang, Yao
Mesiar, Radko
Agahi, Hamzeh
[J]. INFORMATION SCIENCES, 2010, 180 (14) : 2793 - 2801
[10] On the Chebyshev type inequality for seminormed fuzzy integral
Ouyang, Yao
Mesiar, Radko
[J]. APPLIED MATHEMATICS LETTERS, 2009, 22 (12) : 1810 - 1815

← 1 2 →