Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

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

DOI QR Code

A note on entropy defined by Choquet integral on interval-valued fuzzy sets

구간치 퍼지집합상에서 쇼케이적분에 의해 정의된 엔트로피에 관한 연구

  • Jang, Lee-Chae (Dept, of Mathematics and Computer Science, Konkuk University)
  • 장이채 (건국대학교 컴퓨터응용과학부)
  • Published : 2007.04.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we consider interval-valued fuzzy sets which were suggested by Wang and Li(1998) and Turksen(1986) and investigate entropy defined by Choquet integral on interval-valued fuzzy sets. Furthermore, we discuss some properties of them and give some examples related this entropy. This tool has drawn much attention due to numerous applications areas, such as decision making and information theory on interval-valued fuzzy sets.

본 논문에서 우리는 Wang와 Li(1998)와 Turksen(1986)에 의해 소개된 구간치 퍼지집합을 생각하고 구간치 퍼지집합상에서 쇼케이적분에 의해 정의된 엔트로피를 조사한다. 더욱이, 이러한 엔트로피와 관련된 성질들을 토의하고 간단한 예들을 알아본다. 이 공식은 구간치 퍼지집합상의 결정이론 및 정보이론과 같은 응용 영역에서 중요한 역할을 한다.

Keywords

References

  1. P.Burillo and H. Bustince, Entropy on lntuitionistic fuzzy set, and on interval-valued fuzzy sets, Fuzzy sets and systems Vol. 78, pp.305-316, 1996 https://doi.org/10.1016/0165-0114(96)84611-2
  2. G. Choquet, Theory of capacities, Annales de Institut Fourier Vol.5 pp. 131-295, 1953
  3. Jin-Lum Fan, Yuan-Liang Ma and Wei-Xin Xie, On some properties of distance measures, Fuzzy Sets and Systems VoI.117,pp.355-361, 2001 https://doi.org/10.1016/S0165-0114(98)00387-X
  4. Lee-Chae Jang and Won Joo Kim, Some properties of Choquet distance measures for interval-valued fuzzy numbers, J. of Fuzzy Logic and Intelligent Systems, Vol.15 No.7, pp.789-793, 2005 https://doi.org/10.5391/JKIIS.2005.15.7.789
  5. 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
  6. 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
  7. B. Turksen, Interval-valued fuzzy sets on normal forms, Fuzzy Sets and Systems Vol.20, pp.191-210, 1986 https://doi.org/10.1016/0165-0114(86)90077-1
  8. Liu Xuechang, Entropy, distance measure and similarity measure of fuzzy sets and their relations, Fuzzy Sets and Systems Vol.52, pp.201-227, 1992 https://doi.org/10.1016/0165-0114(92)90050-E
  9. 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
  10. W. Zeng and H. Li, Relationship between similarity measure and entropy of interval-valued fuzzy sets, Fuzzy Sets and Systems Vol. 157, pp.l477-1484, 2006