Generalized Lebesgue integral

被引：26

作者：

Zhang, Qiang ^{[2
]}

Mesiar, Radko ^{[3
,4
]}

Li, Jun ^{[1
]}

Struk, Peter ^{[3
]}

机构：

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

[2] Beijing Inst Technol, Sch Management & Econ, Beijing 100081, Peoples R China

[3] Slovak Univ Technol Bratislava, Dept Math & Descript Geometry, Fac Civil Engn, SK-81368 Bratislava, Slovakia

[4] Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Ostrava 70103 1, Czech Republic

来源：

INTERNATIONAL JOURNAL OF APPROXIMATE REASONING | 2011年 / 52卷 / 03期

关键词：

Pseudo-addition; Pseudo-multiplication; Generalized Lebesgue integral; Pan-integral; FUZZY INTEGRALS; OPERATIONS;

D O I：

10.1016/j.ijar.2010.10.002

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

A new definition of integral-like functionals exploiting the ideas of the Lebesgue integral construction and extending the idea of pan-integrals is given. Some convergence theorems for sequence of measurable functions are discussed. As a result, a theoretical basis for applications of the generalized Lebesgue integral is provided. Several types of integrals known from the literature are shown to be special cases of generalized Lebesgue integral. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：427 / 443

页数：17

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