Issue:New measures of entropy for intuitionistic fuzzy sets

shortcut

http://ifigenia.org/wiki/issue:nifs/11/2/12-20

Title of paper: New measures of entropy for intuitionistic fuzzy sets Author(s): Eulalia Szmidt Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland szmidt@ibspan.waw.pl Janusz Kacprzyk Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, OL-447 Warsaw, Poland kacprzyk@ibspan.waw.pl Presented at: 9th ICIFS, Sofia, 7-8 May 2005 Published in: Conference proceedings, "Notes on IFS", Volume 11 (2005) Number 2, pages 12—20 Download:  PDF (167  Kb, File info) Abstract: We propose the new measures of entropy for intuitionistic fuzzy sets. This paper is in a sense a continuation of our previous paper on entropy of intuitionistic fuzzy sets — the inferences are based on the same two types of distances as previously — to the farer and to the nearer crisp elements. But instead of the ratio of these distances we examine their difference. The distances are calculated using the formulas for the normalized Hamming distance, and the normalized Euclidean distance. In the case of the Hamming distance we obtain simpler formulas than in our previous paper. We show some special properties for the formulas when Hamming distance is applied. We also suggest π-entropy, a function strongly accounting for the lack of knowledge as to the membership and non-membership. Keywords: Fuzzy sets, Intuitionistic fuzzy sets, Entropy, Similarity References: Atanassov K. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87—96. Atanassov K. (1999), Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag. Burillo P. and Bustince H. (1996). Entropy of intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets and Systems, 78, 305—316. Cornelis Ch. and Kerre E. (2003). Inclusion measures in intuitionistic fuzzy set theory. Proc. of ECSQARU’ 2003. Higashi M. and Klir G. (1982). On measures of fuzziness and fuzzy complements. Int. J. Gen. Syst., 8, 169—180. De Luca A. and Termini S. (1972). A definition of a non-probabilistic entropy in the setting of fuzzy sets theory. Inform. and Control, 20, 301—312. Fan J. and W. Xie (1999). Distance measure and induced fuzzy entropy. Fuzzy Sets and Systems, 104, 305—314. Fan J-L., Ma Y-L. and Xie W-X. (2001). On some properties of distance measures. Fuzzy Sets and Systems, 117, 355—361. Fan J-L. and Ma Y-L. (2002). Some new fuzzy entropy formulas. Fuzzy sets and Systems, 128, 277—284. Hu Q. and Yu D. (2004). Entropies of fuzzy indiscernibility relation and its operations. Int. J. of Uncertainty, Knowledge-Based Systems, 12 (5), 575—589. Hung W-L. (2003). A note on entropy of intuitionistic fuzzy sets. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 11 (5), 627—633. Jaynes E.T. (1979). Where do we stand on maximum entropy? In: The Maximum Entropy Formalism, Levine and Tribus (Eds.), MIT Press, Cambridge Mass. Kosko B. (1986) Fuzzy entropy and conditioning. Inform. Sciences, 40, 165—174. Pal N.R. and Bezdek J.C. (1994). Measuring fuzzy uncertainty. IEEE Trans. on Fuzzy Systems, 2 (2), 107—118. Pal N.R. and Pal S.K. (1991). Entropy: a new definition and its applications. IEEE Trans. on Systems, Man, and Cybernetics, 21 (5), 1260—1270. Szmidt E. (2000) Applications of Intuitionistic Fuzzy Sets in Decision Making. (D.Sc. dissertation) Techn. Univ., Sofia, 2000. Szmidt E. and Baldwin J. (2003) New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs, 9 (3), 60—76. Szmidt E. and Baldwin J. (2004) Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs, 10 (3), 15—28. Szmidt E. and Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, 114 (3), 505—518. Szmidt E. and Kacprzyk J. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118 (3), 467—477. Szmidt E. and Kacprzyk J. (2002). An Intuitionistic Fuzzy Set Base Approach to Intelligent Data Analysis (an application to medical diagnosis). In A. Abraham, L. Jain, J. Kacprzyk (Eds.): Recent Advances in Intelligent Paradigms and Applications. Springer-Verlag, 57—70. Szmidt E. and Kacprzyk J. (2004) Similarity of intuitionistic fuzzy sets and the Jaccard coeIcient. IPMU 2004, Perugia, Italy, 1405—1412. Szmidt E. and Kacprzyk J. (2005). A new concept of similarity measure for intuitionistic fuzzy sets and its use in group decision making. In press. Tversky A. (1977). Features of similarity. Psychol. Rev., 84, 327—352. Yager R.R. (1997). On measures of fuzziness and negation. Part I: Membership in the unit interval. Int. J. Gen. Syst., 5, 221—229. L.A. Zadeh (1965). Fuzzy sets. Information and Control, 8, 338—353. Citations: Issue:Intuitionistic fuzzy sets in group decision making – A novel approach ‎ (← links) The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.