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