Title of paper:
|
A concept of entropy for intuitionistic fuzzy sets
|
Author(s):
|
Eulalia Szmidt
|
Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
|
szmidt@ibspan.waw.pl
|
Janusz Kacprzyk
|
Systems Research Institute Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
|
kacprzyk@ibspan.waw.pl
|
|
Published in:
|
"Notes on IFS", Volume 3 (1997) Number 2, pages 41—52
|
Download:
|
PDF (4446 Kb, File info)
|
Abstract:
|
A non-probabilistic-type entropy measure for intuitionistic fuzzy sets is proposed. It is a result of a geometrical interpretation of intuitionistic fuzzy sets and uses a ratio of distances between them proposed in [18]. It is also shown that the proposed measure can be defined in terms of the ratio of intuitionistic fuzzy cardinalities of F ∩ Fc and F ∪ Fc.
|
Keywords:
|
distance between intuitionistic fuzzy set, cardinality of intuitionistic fuzzy set, entropy of intuitionistic fuzzy set.
|
References:
|
- Atanassov K. (1986) - Intuitionistic fuzzy sets. Fuzzy Sets and Systems, Vol. 20, No. 1, 87-96
- Atanassov K. (1989) - More on intuitionistic fuzzy sets. Fuzzy Sets and Systems, 33, No. 1, 37-46.
- Atanassov K. (1994) - New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems, 61, No. 2, 137-142.
- Atanassov K. (1994) - Operators over interval valued intuitionistic fuzzy sets. Fuzzy Sets and Systems, 64, 159-174.
- Atanassov K. - Intuitionistic Fuzzy Sets: Theory and Applications. (Textbook; to appear).
- Jaynes E.T. (1979) - Where do we stand on maximum entropy? In: The Maximum Entropy Formalism, ed. By Levine and Tribus, MIT Press, Cambridge Mass.
- Kacprzyk J. (1997) - Multistage Fuzzy Control. J. Wiley.
- Kaufmann A. (1975) - Introduction to the Theory of Fuzzy Subsets - Vol.1: Fundamental Theoretical Elements. Academic Press, New York.
- Klir G.J. and Wierman M.J. (1997) - Uncertainty - Based Information Elements of Generalized Information Theory. Lecture Notes in Fuzzy Mathematics and Computer Science, 3, Creighton University, Omaha, Nebraska 68178 USA.
- Kosko B. (1986) - Fuzzy Entropy and Conditionong. Information Sciences, vol. 40, 2, 165-174.
- Kosko B. (1990) - Fuzziness vs. Probability. Int. Journal of General Systems, vol. 17, 2-3, 211-240.
- Kosko B. (1997) - Fuzzy Engineering. Prentice-Hall.
- 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.
- Szmidt E. and Kacprzyk J. (1996) - Intuitionistic fuzzy sets in group decision making. Notes on IFS, Vol. 2, 1, 15-32.
- Szmidt E. and Kacprzyk J. (1996) - Group decision making via intuitionistic fuzzy sets. FUBEST'96, October 9-11, Sofia, Bulgaria, 107-112.
- Szmidt E. and Kacprzyk J. (1996) - Remarks on some applications of intuitionistic fuzzy sets in decision making. Notes on IFS, vol.2, 3, 22-31.
- Szmidt E. and Kacprzyk J. (1997) -Intuitionistic fuzzy sets for more realistic group decision making. Proc. of TRANSITION'97, June 18-21, Warsaw, Poland, 430-433.
- Szmidt E. and Kacprzyk J. - On distances between intuitionistic fuzzy sets. To appear.
- Yager R. R. (1979) - On the measure of fuzziness and negation. Part I: Membership in the unit interval. Internat. J. Gen. Systems, Vol. 5, 189-200.
- Zadeh L. A. (1965) - Fuzzy sets. Information and Control, 8, 338-353.
- Zadeh L.A. (1965) - Fuzzy Sets and Systems. In: Proceedings of the Symposium on Systems Theory. pp. 29-37. Politechnic Institute of Brooklyn. N.Y.
- Zadeh L. A. (1983) - A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. Vol. 9, 1, 149-184.
- Zadeh L. A. (1983) - The role of fuzzy logic in the management of uncertainty in expert systems. Fuzzy Sets and Systems, 11, 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.
|
|