Issue:Cardinality and entropy of IF sets

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Title of paper: Cardinality and entropy of IF sets Author(s): Pavol Král Faculty of Economics, Matej Bel University, Department of Mathematics, Tajovskeho 10 974 01 Banska Bystrica, Slovakia pavol.kral@umb.sk Presented at: 9th ICIFS, Sofia, 7-8 May 2005 Published in: Conference proceedings, "Notes on Intuitionistic Fuzzy Sets", Volume 11 (2008) Number 3, pages 78—87 Download:  PDF (4979  Kb, File info) Abstract: There are two basic different approaches to the entropy of finite IF sets. One can be found in [3], the other in [17]. The paper # has presented the possible extensions of axiomatic theory of the scalar cardinality of finite fuzzy sets developed by Wygralak (see [23]) to the case of IF sets. The aim of our contribution is to show the connections of cardinalities of finite IF sets to both entropies. We will show that the entropy in both sense can be derived from appropriate cardinality. Keywords: cardinality, IF sets, entropy References: Atanassov, K., T. (1986) Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87-96. Atanassov, K., T., Gargov, G. (1989) Interval valued intuitionistic fuzzy sets, Fuzzy sets and Systems 31, 343-349. Burillo, P., Bustince, H.,(1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets, Fuzzy Sets and Systems 78, 305-316. De Luca, A., Termini, S.(1972) A definition of non-probabilistic entropy in the setting of fuzzy sets theory Inform. Control 20, 301-312. Deschrijver, G., Cornelis, C., Kerre, E. E. (2003) Intuitionistic fuzzy connectives revisited, Proceedings of the 9th Iternational Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pages 1839-1844. Dubois, D., Prade, D. (1985) Fuzzy cardinality and the modeling of imprecise quantification Fuzzy Sets and Systems 16, 199-230. Gottwald, S. (1980) A note on fuzzy cardinals Kybernetika 16, 156-158. Kaufmann, A. (1975) Introduction to the Theory of Fuzzy Subsets, Academic Press, New York. Kaufmann, A. (1977) Introduction a la theorie des sous-ensembles flous Complement et Nouvelles Applications 4 Kosko, B. (1986) Fuzzy entropy and conditioning, Inform. Sci. 40 (2), 165-174. Kosko, B. (1990) Fuzziness vs. probability, Internat J. General Systems 17 (2-3), 211-240. Kosko, B. (1997) Fuzzy Engineering, Prentice-Hall, Englewood Cliffs, NJ. Král, P. (2004) On the Scalar Cardinality of IF Sets. Journal of Electrical Engineering, volume 55, 83 - 86. Loo, S. G. (1977), Measures of fuzziness, Cybernetica 20, 201-210. Ralescu, D.(1995) Cardinality, quantifiers, and the aggregation of fuzzy criteria Fuzzy Sets and Systems 69, 355-365. Sambuc, R.(1975) Functions Ф-flous. Aplication a l'aide au diagnostic en pathologie thyro-dene, Theese, Universite de Marseille. Szmidt, E., Kacprzyk J. (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 110: 467-477 Trillas, E., Riera, T. (1978) Entropies in finite fuzzy sets, Inform. Sci. 15, 159-168. Yager, R. R. (1982) On measure of fuziness and fuzzy complements, Internat. J. General Systems 8, 169-180. Wygralak, M. (2000) An axiomatic approach to scalar cardinalities of a fuzzy set Fuzzy Sets and Systems 110, 175-176. Wygralak, M. (1997) Cardinalities of fuzzy sets evaluated by single cardinals Proc. IFSA Congress Praha, 73 - 77 Wygralak, M. (1999) Question of cardinality of finite fuzzy sets Fuzzy Sets and Systems 102, 185-210. Wygralak, M. (2003) Cardinalities of Fuzzy Sets. Studies in Fuzziness and Soft Computing 118, Springer-Verlag, Berlin, Heidelberg. Zadeh, L. A. (1965) Fuzzy sets, Inform, and Control 8, 338-353. Zadeh, L. A. (1965) Fuzzy sets and systems, Proceedings of the Symposium on on Systems Theory, Polytechnic Institute of Brooklyn, NY Citations: The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.