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Issue:Probability measures for intuitionistic fuzzy sets: Difference between revisions

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  | author          = Eulalia Szmidt
  | author          = Eulalia Szmidt
  | institution    = Systems Research lnstitute - Polish Academy of Sciences
  | institution    = Systems Research lnstitute - Polish Academy of Sciences
  | address        = ul. Newelska 6, OL-447 Warsaw, Poland
  | address        = ul. Newelska 6, 01-447 Warsaw, Poland
  | email-before-at = szmidt
  | email-before-at = szmidt
  | email-after-at  = ibspan.waw.pl
  | email-after-at  = ibspan.waw.pl
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  | author          = Janusz Kacprzyk
  | author          = Janusz Kacprzyk
  | institution    = Systems Research lnstitute - Polish Academy of Sciences
  | institution    = Systems Research lnstitute - Polish Academy of Sciences
  | address        = ul. Newelska 6, OL-447 Warsaw, Poland
  | address        = ul. Newelska 6, 01-447 Warsaw, Poland
  | email-before-at = kacprzyk
  | email-before-at = kacprzyk
  | email-after-at  = ibspan.waw.pl
  | email-after-at  = ibspan.waw.pl
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{{issue/data
{{issue/data
  | conference      = Third [[ICIFS|International Conference on IFSs]], Sofia, 16-17 October 1999
  | conference      = Third [[ICIFS|International Conference on IFSs]], Sofia, 16-17 October 1999
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/05/3|"Notes on IFS", Volume 5 (1999) Number 3]], pages 19—28
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/05/3|"Notes on Intuitionistic Fuzzy Sets", Volume 5 (1999) Number 3]], pages 19—28
  | file            = NIFS-05-3-19-28.pdf
  | file            = NIFS-05-3-19-28.pdf
  | format          = PDF
  | format          = PDF
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  | 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.
  | 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 imprecission is modelled by intuitionistic fuzzy sets and uncerainty is modelled by probability theory. Both types of information imperfection are discussed and expressed by common formulas
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]]
  | keywords        = [[fuzzy set]], [[intuitionistic fuzzy set]], fuzzy event, intuitionistic fuzzy event, fuzzy probability, [[intuitionistic fuzzy probability]]

Latest revision as of 11:05, 29 August 2024

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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:
  1. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) '87-96.
  2. K. Atanassov, More on intuitionistic fuzzy sets, Fuzzy Sets and Systems 33 (1989) 37-46.
  3. K. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994a) 137-142.
  4. K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems 64 (1994b) 159-174.
  5. K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications (to appear).
  6. T. Gerstenkorn and J. Manko, Probability of fuzzy intuitionistic sets, BUSEFAL, Vol.45, (1990), 128-136.
  7. E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets in group decision making, Notes on IFS 2 (1996a) 15-32.
  8. E. Szmidt and J. Kacprzyk, Group decision making via intuitionistic fuzzy sets, Proceeding of FUBEST'96 (Sofia, Bulgaria, 1996b) 107-112.
  9. Е. Szmidt and J. Kacprzyk, Remarks on some applications of intuitionistic fuzzy sets in decision making, Notes on IFS 2 (1996c) 22-31.
  10. E. Szmidt and J. Kacprzyk, Intuitionistic fuzzy sets for more realistic group decision making, Proceedings of TRANSITIONS'97 (Warsaw, Poland, 1997a) 430-433.
  11. E. Szmidt and J. Kacprzyk, On measuring distances between intuitionistic fuzzy sets, Notes on IFS 3 (1997b) 1-13.
  12. Szmidt E. and Kacprzyk J. (1998a) Intuitionistic fuzzy linguistic quantifiers. Notes on IFS, Vol.3, No.5. pp. 111-122.
  13. 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.
  14. 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.
  15. Szmidt E. and Kacprzyk J. (1998d) Entropy for Intuitionistic Fuzzy Sets. Accepted for publication in Fuzzy Sets and Systems.
  16. Szmidt E. and Kacprzyk J. (1998e) Distances Between Intuitionistic Fuzzy Sets. Accepted for publication in Fuzzy Sets and Systems.
  17. 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.
  18. 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.
  19. L.A. Zadeh (1965) Fuzzy sets. Information and Control, 8 338-353.
  20. L.A. Zadeh (1968) Probability measures of fuzzy events. J.Math.Anal.Appl. Vol.23, pp..421-427.
  21. L.A. Zadeh (1983a) A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl., Vol. 9, No. 1, pp. 149-184.
  22. 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.
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