Proceedings of the Korean Institute of Intelligent Systems Conference (한국지능시스템학회:학술대회논문집)
- 2007.11a
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- Pages.195-198
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- 2007
On Lebesgue-type theorems for interval-valued Choquet integrals with respect to a monotone set function.
단조집합함수에 의해 정의된 구간치 쇼케이적분에 대한 르베그형태 정리에 관한 연구
- Jang, Lee-Chae (Dept. of Mathematics and Computer Science, Konkuk University EECS, Kyungpook University) ;
- Kim, Tae-Kyun (Dept. of Mathematics and Computer Science, Konkuk University EECS, Kyungpook University)
- Published : 2007.11.02
Abstract
In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.
Keywords
- monotone set functions;
- interval-valued functions;
- Choquet integrals;
- fuzzy integrals;
- Lebesgue's theorems;
- monotone convergence theorems