Towards More Human Consistent Reasoning via Intuitionistic Fuzzy Sets

  • Eulalia Szmidt
  • Janusz Kacprzyk
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 19)


Intuitionistic fuzzy sets (Atanassov [1], [2]), due to of an additional degree of freedom, can be viewed as a generalization of fuzzy sets. The additional degree of freedom makes a better modelling of imperfect information possible. We propose the me of intuitionistic fuzzy sets for a more human consistent reasoning under imprecise knowledge. An example of a medical database is considered. Employing intuitionistic fuzzy sets, we can express a hesitation concerning both the patients and illnesses. An illness for each patient is found by looking for the smallest distance [cf. Szmidt and Kacprzyk [5], [8]] between symptoms that are characteristic for a patient, and symptoms describing illnesses. Our new approach can help avoid drawbacks of the max-min-max rule that is usually employed [cf. De, Biswas and Roy [3]].


Imperfect Information Fuzzy Relation Fuzzy Preference Relation Fuzzy Relation Equation Stomach Problem 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Atanassov K. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87–96.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Atanassov K. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag.MATHGoogle Scholar
  3. 3.
    De S.K., Biswas R. and Roy A.R. (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems, Vol. 117, No. 2, pp. 209–213.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Sanchez E. (1976) Resolution of composition fuzzy relation equations. Inform. Control, Vol. 30, pp. 38–48.MATHCrossRefGoogle Scholar
  5. 5.
    Szmidt E. and Kacprzyk J. (1997) On measuring distances between intuitionistic fuzzy sets, Notes on IFS, Vol. 3, No. 4, pp. 1–13.MathSciNetMATHGoogle Scholar
  6. 6.
    Szmidt E. and Kacprzyk J. (1998b) Group Decision Making under Intuitionistic Fuzzy Preference Relations. Proceedings of the 7th Int. Conference IPMU’98 (Paris, La Sorbonne, July 6–10), pp. 172–178.Google Scholar
  7. 7.
    Szmidt E. and Kacprzyk J. (1998c) Applications of Intuitionistic Fuzzy Sets in Decision Making. Proceedings of the 8th Congreso EUSFLAT’99 (Pamplona, Univ. De Navarra, September 8–10), pp. 150–158.Google Scholar
  8. 8.
    Szmidt E. and J. Kacprzyk J. (2000) Distances between intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 114, No. 3, pp. 505–518.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Szmidt E. and Kacprzyk J. (2000) On Measures on Consensus Under Intuitionistic Fuzzy Relations. Proc. of Eight Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems IPMU 2000, Madrid, July 3–7, 2000, pp. 1454–1461.Google Scholar
  10. 10.
    Szmidt E. and Kacprzyk J. (2001) Distance from consensus under Intuitionistic Fuzzy Preferences. In: Proc. on Eurofuse Workshop on Preference Modelling and Applications, Granada, Spain, April 25–27, 2001, pp. 73–77.Google Scholar
  11. 11.
    Zadeh L.A. (1965) Fuzzy sets. Information and Control Vol. 8, pp. 338–353.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Zadeh L.A. and Kacprzyk J. (1999) (Eds.) Computing with words in information/intelligent systems. 1. Foundations. 2. Applications. Physica-Verlag. Heidelberg, New York.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Eulalia Szmidt
    • 1
  • Janusz Kacprzyk
    • 1
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland

Personalised recommendations