Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

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

  • 장이채 (건국대학교 컴퓨터응용과학부 전산수학) ;
  • 김태균 (경북대 전자전기컴퓨터학부)
  • Published : 2007.12.25
Download PDF
⟨ Previous Next ⟩

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

References

  1. L.C. Jang and J,S. Kwon, On the representation of Choquet integrals of set-valued functions and null sets, Fuzzy Sets and Systems Vol.112 pp.233-239, 2000 https://doi.org/10.1016/S0165-0114(98)00184-5
  2. L.C. Jang, Some characterizations of interval- valued Choquet price functionals, J. of Korea Fuzzy Logic and Intelligent Systems Society Vol.16, No.2, pp.247-251, 2006 https://doi.org/10.5391/JKIIS.2006.16.2.247
  3. L.C. Jang, A note on the monotone interval- valued set function defined by interval-valued Choquet integral, Commun. Korean Math Soc. Vol.22, No.2, pp.227-234, 2007 https://doi.org/10.4134/CKMS.2007.22.2.227
  4. Jinjie Song and Jun Li, Lebesgue theorems in non-additive measure theory, Fuzzy Sets and Systems Vol.149, pp.543-548, 2005 https://doi.org/10.1016/j.fss.2004.03.022
  5. Deli Zhang and Zixiao Wang, Fuzzy integrals of fuzzy-valued functions, Fuzzy Sets and Systems Vol.54, pp.63-67, 1993 https://doi.org/10.1016/0165-0114(93)90361-K
  6. D. Zhang, C.Guo and D. Liu, Set-valued Choquet integrals revisited, Fuzzy Sets and Systems Vol.147, pp.475-485, 2004 https://doi.org/10.1016/j.fss.2004.04.005
  7. Z. Wang and G.J. Klir, Fuzzy measure theory, Plenum Press, New York, 1992