DOI QR코드

DOI QR Code

Analysis of Fuzzy Entropy and Similarity Measure for Non Convex Membership Functions

  • Lee, Sang-H. (School of Mechatronics, Changwon National University) ;
  • Kim, Sang-Jin (School of Mechatronics, Changwon National University)
  • Published : 2009.03.01

Abstract

Fuzzy entropy is designed for non convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

Keywords

References

  1. D. Bhandari, N. R. Pal, "Some new information measure of fuzzy sets," Inform. Sci. vol. 67, pp. 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, vol. 72, pp. 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, vol. 52, pp. 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. vol. 36, pp.284-295, 1989
  6. S.H. Lee, K.B. Kang and S.S. Kim, "Measure offuzziness with fuzzy entropy function," Journal of Fuzzy Logic and lntelligent Systems, vol. 14, no. 5, pp. 642-647, 2004 https://doi.org/10.5391/JKIIS.2004.14.5.642
  7. S.H. Lee, S.P. Cheon, and Jinho Kim, "Measure of certainty with fuzzy entropy function," LNAI, vol. 4114, pp. 134-139, 2006 https://doi.org/10.1007/11816171_17
  8. J.S.R. Jang, C.T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing, Prentice Hall, Upper Saddle River, 1997
  9. J.M. Garibaldi, Musikasuwan, S. Ozen, T. John, R.I., "A case study to illustrate the use of non convex membership functions for linguistic tenns", 2004 lEEE International Comference on Fuzzy Systems, vol.3, pp. 1403-1408, 2004
  10. J. L. Fan, W. X. Xie, "Distance measure and induced fuzzy entropy," Fuzzy Set and Systems, vol. 104, pp. 305-314, 1999 https://doi.org/10.1016/S0165-0114(99)80011-6
  11. H.J. Park, S.S. Kim ans S.H. Lee, "Similarity measure construction for non convex fuzzy membership function," Journal of KIIS, vol. 18, no. 1, pp. 145-149, 2008 https://doi.org/10.5391/JKIIS.2008.18.1.145