DOI QR코드

DOI QR Code

Construction of Fuzzy Entropy and Similarity Measure with Distance Measure

거리 측도를 이용한 퍼지 엔트로피와 유사측도의 구성

  • Published : 2005.10.01

Abstract

The fuzzy entropy is proposed for measuring of uncertainty with the help of relation between distance measure and similarity measure. The proposed fuzzy entropy is constructed through a distance measure. In this study, Hamming distance measure is employed for a distance measure. Also a similarity measure is constructed through a distance measure for the measure of similarity between fuzzy sets or crisp sets and the proposed fuzzy entropies and similarity measures are proved.

모호함의 측도를 위하여 퍼지 엔트로피와 거리측도 그리고 유사측도와의 관계를 이용하여 새로운 퍼지 측도를 제안하였다. 제안된 퍼지 엔트로피는 거리측도를 이용하여 구성된다. 거리측도는 일반적으로 사용되는 해밍 거리를 이용하였다. 또한 집합사이의 유사성을 측정하기 위한 유사측도를 거리 측도를 이용하여 구성하였고, 제안한 퍼지 엔트로피와 유사측도를 증명을 통하여 타당성을 확인하였다.

Keywords

References

  1. D. Bhandari, N. R. Pal, 'Some new information measure of fuzzy sets,' Inform. Sci. 67, 209-228, 1993 https://doi.org/10.1016/0020-0255(93)90073-U
  2. A. Ghosh, 'Use of fuzziness measure in layered networks for object extraction: a generalization,' Fuzzy Sets and Systems, 72, 331-348, 1995 https://doi.org/10.1016/0165-0114(94)00291-E
  3. B. Kosko, Neural Networks and Fuzzy Systems, Prentice-Hall, Englewood Cliffs, NJ, 1992
  4. Liu Xuecheng, 'Entropy, distance measure and similarity measure of fuzzy sets and their relations,' Fuzzy Sets and Systems, 52, 305-318, 1992 https://doi.org/10.1016/0165-0114(92)90239-Z
  5. N.R. Pal, S.K. Pal, 'Object-background segmentation using new definitions of entropy,' IEEE Proc. 36, 284-295, 1989
  6. J. L. Fan, W. X. Xie, 'Distance measure and induced fuzzy entropy,' Fuzzy Set and Systems, 104, 305-314, 1999 https://doi.org/10.1016/S0165-0114(99)80011-6
  7. J. L. Fan, Y. L. Ma, and W. X. Xie, 'On some properties of distance measures,' Fuzzy Set and Systems, 117, 355-361, 2001 https://doi.org/10.1016/S0165-0114(98)00387-X
  8. S.H. Lee and S.S. Kim, 'On some properties of distance measures and fuzzy entropy,' Proceedings of KFIS Fall Conference, 2002, 9-12