Abstract
Study of fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) was proposed and analyzed. Unlike fuzzy set, IFSs contain uncertainty named hesitance, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of many entropy definitions. By considering different fuzzy entropy definitions, fuzzy entropy on IFSs is designed and discussed. Similarity measure was also presented and its usefulness was verified to evaluate degree of similarity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ZADEH L A. Fuzzy sets and systems [C]// Proc Symp on Systems Theory. New York: Polytechnic Institute of Brooklyn, 1965: 29–37.
PAL N R, PAL S K. Object-background segmentation using new definitions of entropy [J]. IEEE Proc, 1989, 36: 284–295.
KOSKO B. Neural networks and fuzzy systems [M]. Englewood Cliffs, NJ: Prentice-Hall, 1992: 152–158.
LIU Xue-cheng. Entropy, distance measure and similarity measure of fuzzy sets and their relations [J]. Fuzzy Sets and Systems, 1992, 52: 305–318.
BHANDARI D, PAL N R. Some new information measure of fuzzy sets [J]. Inform Sci, 1993, 67: 209–228.
DELUCA, TERMINI S. A definition of nonprobabilistic entropy in the setting of fuzzy entropy [J]. J General Systems, 1972, 5: 301–312.
HSIEH C H, CHEN S H. Similarity of generalized fuzzy numbers with graded mean integration representation [C]// Proc 8th Int Fuzzy Systems Association World Congr. Taipei, 1999: 551–555.
CHEN S J, CHEN S M. Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers [J]. IEEE Trans on Fuzzy Systems, 2003, 11(1): 45–56.
LEE S H, PEDRYCZ W, GYOYONG SOHN. Design of similarity and dissimilarity measures for fuzzy sets on the basis of distance measure [J]. International Journal of Fuzzy Systems, 2009, 11: 67–72.
LEE S H, RYU K H, SOHN G Y. Study on entropy and similarity measure for fuzzy set [J]. IEICE Trans Inf & Syst, 2009, E92-D: 1783–1786.
LEE S H, KIM S J, JANG N Y. Design of fuzzy entropy for non convex membership function [J]. Communications in Computer and Information Science, 2008, 15: 55–60.
ATANASSOV K. Intuitionistic fuzzy sets [J]. Fuzzy Set and System, 1986, 20: 87–96.
ATANASSOV K. Intuitionistic fuzzy sets: Theory and applications [M]. Heidelberg: Physica-Verlag, 1999: 128–155.
ATANASSOV K. New operations defined over the intuitionistic fuzzy sets [J]. Fuzzy Set and Sysem, 1994, 61: 137–142.
GAU W L, BUEHRER D J. Vague sets [J]. IEEE Trans Syst Man Cybernet, 1993, 23(2): 610–614.
BURILLO P, BUSTINCE H. Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets [J]. Fuzzy Sets and Systems, 1996, 78: 305–316.
LI Deng-feng, CHENG Chun-tian. New similarity measure of intiotionistic fuzzy sets and application to pattern recognitions [J]. Pattern Recognotion Letter, 2002, 23: 221–225.
LIN Yan-hong, OLSON D L, QIN Zheng. Similarity measures between intuitionistic fuzzy (vague) set: A comparative analysis [J]. Pattern Recognition Letter, 2007, 28: 278–285.
HUNG W L, YANG M S. Fuzzy entropy on inttuitionistic fuzzy sets [J]. International Journal of Intelligent Systems, 2006, 21: 443–451.
SZMIDT E, KACPRZYK J. Entropy for intuitionistic fuzzy sets [J]. Fuzzy Sets and Systems, 2001, 118: 467–477.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(ER120001) supported by Development of Application Technology BioNano Super Composites, Korea
Rights and permissions
About this article
Cite this article
Park, JH., Hwang, JH., Park, WJ. et al. Similarity measure on intuitionistic fuzzy sets. J. Cent. South Univ. 20, 2233–2238 (2013). https://doi.org/10.1007/s11771-013-1729-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-013-1729-y