Issue:Probability measures for intuitionistic fuzzy sets

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http://ifigenia.org/wiki/issue:nifs/05/3/19-28

Title of paper: Probability measures for intuitionistic fuzzy sets Author(s): Eulalia Szmidt Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland szmidt@ibspan.waw.pl Janusz Kacprzyk Systems Research lnstitute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland kacprzyk@ibspan.waw.pl Presented at: Third International Conference on IFSs, Sofia, 16-17 October 1999 Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 5 (1999) Number 3, pages 19—28 Download:  PDF (6580  Kb, File info) Abstract: A concept of a probability measure for intuitionistic fuzzy sets is introduced. The solution is given by an interval and is consistent with the probability measure proposed by Zadeh for fuzzy sets. The presented considerations seem to be crucial in decision making where imperfection of information is a rule. There are many aspects of information imperfection and among them uncertainty (randomness) and imprecision (fuzziness) are the most important. In this article we assume that imprecision is modelled by intuitionistic fuzzy sets and uncertainty is modelled by probability theory. Both types of information imperfection are discussed and expressed by common formulas Keywords: fuzzy set, intuitionistic fuzzy set, fuzzy event, intuitionistic fuzzy event, fuzzy probability, intuitionistic fuzzy probability References: K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) '87-96. K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33 (1989) 37-46. K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994a) 137-142. K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 64 (1994b) 159-174. K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications (to appear). T. Gerstenkorn and J. Manko, Probability of fuzzy intuitionistic sets, BUSEFAL, Vol.45, (1990), 128-136. E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, Notes on IFS 2 (1996a) 15-32. E. Szmidt and J. Kacprzyk, Group decision making via intuitionistic fuzzy sets, Proceeding of FUBEST'96 (Sofia, Bulgaria, 1996b) 107-112. Е. Szmidt and J. Kacprzyk, Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS 2 (1996c) 22-31. E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets for more realistic group decision making, Proceedings of TRANSITIONS'97 (Warsaw, Poland, 1997a) 430-433. E. Szmidt and J. Kacprzyk, On measuring distances between intuitionistic fuzzy sets, Notes on IFS 3 (1997b) 1-13. Szmidt E. and Kacprzyk J. (1998a) Intuitionistic fuzzy linguistic quantifiers. Notes on IFS, Vol.3, No.5. pp. 111-122. Szmidt E. and Kacprzyk J. (1998b) A Fuzzy Set Corresponding to an Intuitionistic Fuzzy Set. Int. Journal of Uncertainty and Knowledge Based Systems, Vol.6, No.5, pp.427-435. Szmidt E. and Kacprzyk J. (1998c) Intuitionistic fuzzy set theory and mass assignment theory: Some relations. Notes on IFS, Vol.4, No.1, pp. 1-7. Szmidt E. and Kacprzyk J. (1998d) Entropy for Intuitionistic Fuzzy Sets. Accepted for publication in Fuzzy Sets and Systems. Szmidt E. and Kacprzyk J. (1998e) Distances Between Intuitionistic Fuzzy Sets. Accepted for publication in Fuzzy Sets and Systems. Szmidt E. and Kacprzyk J. (1998f) Group Decision Making under Intuitionistic Fuzzy Preference Relations. Proceedings of the 7th Int. Conference IPMU'98 (Paris, La Sor-bonne, July 6-10), pp. 172-178. Szmidt E. and Kacprzyk J. (1998g) Applications of Intuitionistic Fuzzy Sets in Decision Making. Proceedings of the 8th Congreso EUSFLAT'9 (Pamplona, Univ. De Navarra, September 8-10), pp. 150-158. L.A. Zadeh (1965) Fuzzy sets. Information and Control, 8 338-353. L.A. Zadeh (1968) Probability measures of fuzzy events. J.Math.Anal.Appl. Vol.23, pp..421-427. L.A. Zadeh (1983a) A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl., Vol. 9, No. 1, pp. 149-184. L.A. Zadeh (1983b) The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems, Vol. 11, pp. 199-227. 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.