A New Heuristic Algorithm of Possibilistic Clustering Based on Intuitionistic Fuzzy Relations

  • Janusz KacprzykEmail author
  • Jan W. Owsiński
  • Dmitri A. Viattchenin
  • Stanislau Shyrai
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


This paper introduces a novel intuitionistic fuzzy set-based heuristic algorithm of possibilistic clustering. For the purpose, some remarks on the fuzzy approach to clustering are discussed and a brief review of intuitionistic fuzzy set-based clustering procedures is given, basic concepts of the intuitionistic fuzzy set theory and the intuitionistic fuzzy generalization of the heuristic approach to possibilistic clustering are considered, a general plan of the proposed clustering procedure is described in detail, two illustrative examples confirm good performance of the proposed algorithm, and some preliminary conclusions are formulated.


Intuitionistic fuzzy set Intuitionistic fuzzy tolerance Similarity measure Clustering 



The authors are grateful to Prof. Eulalia Szmidt for her useful remarks and fruitful discussions during the paper preparation.


  1. 1.
    Krishnapuram, R., Keller, J.M.: A possibilistic approach to clustering. IEEE Trans. Fuzzy Syst. 1(2), 98–110 (1993)CrossRefGoogle Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications. Physica-Verlag, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, K.T.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  5. 5.
    Xu, Z.: Intuitionistic Fuzzy Aggregation and Clustering. Springer, Berlin (2013)zbMATHGoogle Scholar
  6. 6.
    Viattchenin, D.A.: A Heuristic Approach to Possibilistic Clustering: Algorithms and Applications. Springer, Berlin (2013)CrossRefzbMATHGoogle Scholar
  7. 7.
    Viattchenin, D.A., Shyrai, S.: Intuitionistic heuristic prototype-based algorithm of possibilistic clustering. Commun. Appl. Electron. 1(8), 30–40 (2015)CrossRefGoogle Scholar
  8. 8.
    Shyrai, S., Viattchenin, D.A.: Clustering the intuitionistic fuzzy data, detection of an unknown number of intuitionistic fuzzy clusters in the allotment. In: Proceedings of the International Conference on Information and Digital Technologies (IDT’2015), IEEE Service Center, Piscataway, pp. 302–311 (2015)Google Scholar
  9. 9.
    Burillo, P., Bustince, H.: Intuitionistic fuzzy relations (Part I). Mathw. Soft Comput. 2(1), 5–38 (1995)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Burillo, P., Bustince, H.: Intuitionistic fuzzy relations (Part II). Effect of Atanassov’s operators on the properties of the intuitionistic fuzzy relations. Mathw. Soft Comput. 2(2), 117–148 (1995)Google Scholar
  11. 11.
    Hung, W.-L., Lee, J.-S., Fuh, C.-D.: Fuzzy clustering based on intuitionistic fuzzy relations. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 12(4), 513–529 (2004)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Janusz Kacprzyk
    • 1
    Email author
  • Jan W. Owsiński
    • 1
  • Dmitri A. Viattchenin
    • 2
  • Stanislau Shyrai
    • 2
  1. 1.Systems Research Institute Polish Academy of SciencesWarsawPoland
  2. 2.Department of Software Information Technology, Belarusian State University of Informatics and Radio-ElectronicsMinskBelarus

Personalised recommendations