Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

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

DOI QR Code

Some properties of Choquet distance measures for interval-valued fuzzy numbers

구간치 퍼지수 상의 쇼케이 거리측도에 관한 성질

  • Jang, Lee-Chae (Dept. of Mathematics and Computer Science, Konkuk University) ;
  • Kim, Won-Joo (Dept. of Mathematics, Kyunghee University)
  • 장이채 (건국대학교 컴퓨터응용과학부 전산수학전공) ;
  • 김원주 (경희대학교 대학원 수학과)
  • Published : 2005.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

Interval-valued fuzzy sets were suggested for the first time by Gorzalczang(1983) and Turken(19a6). Based on this, Wang and Li offended their operations on interval-valued fuzzy numbers. Recently, Hong(2002) generalized results of Wang and Li and extended to interval-valued fuzzy sets with Riemann integral. In this paper, using Choquet integrals with respect to a fuzzy measure instead of Riemann integrals with respect to a classical measure, we define a Choquet distance measure for interval-valued fuzzy numbers and investigate its properties.

구간치 퍼지집합은 Gorzalczan응(1983)과 Turken(1986)에 의해 처음 제의되었다. 이를 토대로 Wang과 Li는 구간치 퍼지수에 관한 연산으로 일반화하여 연구하였다. 최근에 홍(2002)는 왕과 리의 이론을 기만적분에 의해 구간치 퍼지집합상의 거리측도에 관한 연구를 하였다. 본 논문에서 우리는 일반측도와 관련된 리만적분 대신에 퍼지측도와 관련된 쇼케이적분을 이용한 구간치 퍼지수 상의 쇼케이 거리측도를 정의하고 이와 관련된 성질들을 조사하였다.

Keywords

References

  1. J. Aubin, 'Set-valued analysis', Birkauser Boston, 1990
  2. R .J. Aumann, 'Integrals of set-valued functions', J. Math. Anal. ppl. Vol. 12, pp. 1-12, 1965 https://doi.org/10.1016/0022-247X(65)90049-1
  3. Dug-Hun Hong and Sungho Lee, Some algebraic properties and a distance measure for interval-valued fuzzy numbers, Information Sciences Vol. 148, pp. 1-10, 2002 https://doi.org/10.1016/S0020-0255(02)00265-7
  4. B. Gorzalczany, Approximate inference with interval-valued fuzzy sets - an outline, in Proceedings of Polish Symposium on Interval and Fuzzy Mathematics, Poznan, Poland, 1983, pp.89-95
  5. Lee-Chae Jang. T. Kim, and Jong Duek Jeon, 'On comonotonically additive interval-valued Choquet integrals(II)', KFIS, Vol. 14, No. 1, pp.33-38, 2004
  6. Lee-Chae Jang. T. Kim, and Jong Duek Jeon, On set-valued Choquet integrals and convergence theorem (II), Bull. Kerean Math.Soc., Vol. 20, No. 1, pp.139-147, 2003
  7. Lee-Chae Jang, Interval-valued Choquet integrals and their applications, Journal of Applied Mathematics and Computing, Vol. 16, No.1-2, pp.429-443, 2004
  8. T. Murofushi and M. Sugeno, An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure, Fuzzy Sets and Systems vol. 29 pp. 201-227, 1989 https://doi.org/10.1016/0165-0114(89)90194-2
  9. T. Murofushi and M. Sugeno, A theory of Fuzzy measures: representations, the Choquet integral, and null sets, J. Math. Anal. and Appl. vol. 159 pp. 532-549, 1991 https://doi.org/10.1016/0022-247X(91)90213-J
  10. Y. Narukawa, T.Murofushi and M. Sugeno, Regular fuzzy measure and representation of comonotonically additive functional, Fuzzy Sets and Systems vol.112 pp.177-186, 2000 https://doi.org/10.1016/S0165-0114(98)00138-9
  11. Y. Narukawa, T. Murofushi and M. Sugeno, Extension and representation of comonotonically additive functionals, Fuzzy Sets and Systems, vol. 121, pp. 217-226, 2001 https://doi.org/10.1016/S0165-0114(00)00031-2
  12. B. Turksen, Interval-valued fuzzy sets based on normal forms, Fuzzy Sets and Systems Vol. 20, pp. 191-210, 1986 https://doi.org/10.1016/0165-0114(86)90077-1
  13. G. Wang and X. Li, The applications of interval- valued fuzzy numbers and interval-distribution numbers, Fuzzy Sets and Systems Vol. 98, pp. 331-335, 1998 https://doi.org/10.1016/S0165-0114(96)00368-5

Cited by

  1. A note on Jensen type inequality for Choquet integrals vol.9, pp.2, 2009, https://doi.org/10.5391/IJFIS.2009.9.2.071