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[[Krassimir Atanassov|K. Atanassov]]'s idea of an intuitionistic fuzzy set aimed at improving a formal description of phenomena diverse in meaning in relation to [[Lotfi Zadeh|L. A. Zadeh]]'s original conception of a fuzzy set. In the definition of an intuitionistic fuzzy set there appears a neglected element, the so-called [[intuitionistic fuzzy index]] ([[hesitancy margin]]), being a factor introducing traces of intuition to K. Atanassov's idea. In the present paper, this factor is included in the concept of a probability of intuitionistic fuzzy events.
[[Krassimir Atanassov|K. Atanassov]]'s idea of an intuitionistic fuzzy set aimed at improving a formal description of phenomena diverse in meaning in relation to [[Lotfi Zadeh|L. A. Zadeh]]'s original conception of a fuzzy set. In the definition of an intuitionistic fuzzy set there appears a neglected element, the so-called [[intuitionistic fuzzy index]] ([[hesitancy margin]]), being a factor introducing traces of intuition to K. Atanassov's idea. In the present paper, this factor is included in the concept of a probability of intuitionistic fuzzy events.
  | keywords        = [[Keyword:Fuzzy set|Fuzzy set]], [[Keyword:Intuitionistic fuzzy set|Intuitionistic fuzzy set]], Set relations and operations, [[Keyword:Probability|Probability]], Probability of fuzzy events and of intuitionistic fuzzy events
  | keywords        = [[Fuzzy sets]], [[Intuitionistic fuzzy sets]], Set relations and operations, [[Probability]], [[Fuzzy event]], [[Intuitionistic fuzzy event]], Probability of fuzzy events and of intuitionistic fuzzy events
  | references      = <br />
  | references      =  
# K. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci. 1697184 (in Bulgarian)).
# K. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci. 1697184 (in Bulgarian)).
# K. Atanassov, Intuitionistic fuzzy sets, [[Fuzzy Sets and Systems]], 20, 1986, p. 87-96.
# K. Atanassov, Intuitionistic fuzzy sets, [[Fuzzy Sets and Systems]], 20, 1986, p. 87-96.

Revision as of 20:20, 18 November 2008

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Title of paper: On a hesitancy margin and a probability of intuitionistic fuzzy events
Author(s):
Tadeusz Gerstenkorn
Lodz University, Faculty of Mathematics, ul. Banacha 22, PL 90-238 Lodz, Poland
tadger@math.uni.lodz.pl
Jacek Mańko
Lodz University, Faculty of Mathematics, ul. Banacha 22, PL 90-238 Lodz, Poland
Published in: "Notes on IFS", Volume 7 (2001), Number 1, pages 4-9
Download:  PDF (368  Kb, Info)
Abstract: K. Atanassov's idea of an intuitionistic fuzzy set aimed at improving a formal description of phenomena diverse in meaning in relation to L. A. Zadeh's original conception of a fuzzy set. In the definition of an intuitionistic fuzzy set there appears a neglected element, the so-called intuitionistic fuzzy index (hesitancy margin), being a factor introducing traces of intuition to K. Atanassov's idea. In the present paper, this factor is included in the concept of a probability of intuitionistic fuzzy events.
Keywords: Fuzzy sets, Intuitionistic fuzzy sets, Set relations and operations, Probability, Fuzzy event, Intuitionistic fuzzy event, Probability of fuzzy events and of intuitionistic fuzzy events
References:
  1. K. Atanassov, Intuitionistic fuzzy sets, VII ITKR's Session, Sofia, June 1983 (deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci. 1697184 (in Bulgarian)).
  2. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 1986, p. 87-96.
  3. K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Springer Verlag, 1999.
  4. T. Gerstenkorn, J. Mańko, Bifuzzy probability of intuitionistic fuzzy sets, Notes on Intuitionistic Fuzzy Sets, Volume 4 (1998], Number 1, p. 8-14.
  5. T. Gerstenkorn, J. Mańko, Randomness in the bifuzzy set theory, CASYS, Intern. J. of Computing Anticipatory Systems, Ed. by Danel M. Dubois, Univ. Liège, Belgium. Partial Proc. of CASYS'99 - Third Intern. Conf. on Computing Anticipatory Systems, HEC-Liège, Belgium, August 9-14, 1999, Vol. 7, p. 89-97.
  6. T. Gerstenkorn, J. Mańko, Remarks on the classical probability of bifuzzy events, CASYS, Intern. J. of Computing Anticipatory Systems, Ed. by Danel M. Dubois, Univ. Liège, Belgium. Proc. of CASYS'2000 - Fourth Intern. Conf. on Computing Anticipatory Systems, HEC-Liège, Belgium, August 7-12, 2000.
  7. A. de Luca, S. Termini, A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory, Inform. Control 20, 1972, p. 301-312.
  8. E. Szmidt, J. Kacprzyk, Intuitionistic fuzzy events and their probabilities, "Notes on Intuitionistic Fuzzy Sets", Volume 4 (1998) Number 4, p. 68-72.
  9. L. A. Zadeh, Fuzzy Sets, Inform. Control 8, 1965, p. 338-353.
  10. L. A. Zadeh, Probability measure of fuzzy events, J. Math. Anal. Appl. 23, 1968, p. 421-427.
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