Title: Intuitionistic Fuzzy Topological Polygroups
Author(s): N. Abbasizadeh, B. Davvaz
Pages: 163-179
Cite as:
N. Abbasizadeh, B. Davvaz, Intuitionistic Fuzzy Topological Polygroups, Int. J. Anal. Appl., 12 (2) (2016), 163-179.


The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. Intuitionistic fuzzy topological spaces were introduced by Coker. This paper provides a new connection between algebraic hyperstructures and intuitionistic fuzzy sets. In this paper, we introduce and study the concept of intuitionistic fuzzy subpolygroup and intuitionistic fuzzy topological polygroup. We also investigate some interesting properties of an intuitionistic fuzzy subpolygroup and intuitionistic fuzzy normal subpolygroup.

Full Text: PDF



  1. N. Abbasizadeh and B. Davvaz, Topological polygroups in the framework on fuzzy sets, J. Intell. Fuzzy Syst, 30 (2016) 2811-2820.

  2. N. Abbasizadeh, B. Davvaz and V. Leoreanu-Fotea, Studies on fuzzy topological polygroups, J. Intell. Fuzzy Syst, in press.

  3. N. Abbasizadeh and B. Davvaz, Category of fuzzy topological polygroups, International Journal of Analysis and Applications 11 (2016), 124-136.

  4. T. C. Ahn, K. Hur and K. W. Jang, intuitionistic fuzzy subgroups and level subgroups, International Journal of Fuzzy Logic and Intelligent System 6(3) (2006), 240-246.

  5. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy sets and systems, 20 (1986), 87-96.

  6. R. Biswas Intuitionistic fuzzy subgroups, Mathematical Forum 10 (1996), 39-44.

  7. D. Coker, An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems 88 (1997), 81-89.

  8. S. D. Comer, Polygroups derived from cogroups, J. Algebra 89 (1984), 397-405.

  9. P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.

  10. B. Davvaz and I. Cristea, Fuzzy Algebraic Hyperstructures, Springer, 2015.

  11. B. Davvaz, Isomorphism theorems of polygroups, Bull. Math. Sci. Soc., 33(3) (2010), 11-19.

  12. B. Davvaz, Polygroup Theory and Related System, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.

  13. D. Freni, Une note sur le coeur dun hypergroupe et sur la cloture transitive β ∗ de β, Riv. di Mat. Pura Appl. 8 (1991), 153-156.

  14. F. Gallego, Hausdorffness in intuitionistic fuzzy topological space, Mathware and Soft Computing 10 (2003), 17-22.

  15. M. Jafarpour, H. Aghabozorgi and B. Davvaz, On nilpotent and solvable polygroups, Bulletin of Iranian Mathe- matical Society 39 (2013), 487-499.

  16. Y. B. Jun, On (φ, ψ)- intuitionistic fuzzy mappings, Int. J. Pure Appl. Math. 12(2) (2004), 133-139.

  17. I. M. Hanafy, Completely continuous functions in intuitionistic fuzzy topological spaces, Czechoslovak Math. J. 53 (2003), 793-803.

  18. D. Heidari, B. Davvaz and S. M. S. Modarres, Topological hypergroups in thr sense of Marty, Comm. Algebra 42 (2014), 4712-4721.

  19. K. Hur, S. Y. Jang and H. W. Kang, intuitionistic fuzzy subgroupoids, International Journal of Fuzzy Logic and Intelligent System 3 (2003), 72-77.

  20. K. Hur, S. Y. Jang and H. W. Kang, intuitionistic fuzzy subgroups and cosets, Honam Mathematical J. 26 (2004), 17-41.

  21. M. Koskas, Groupoides, demi-hypergroupes et hypergroupes, J. Math. Pure Appl. 49(9) (1970), 155-192.

  22. S. J. Lee and P. E. Lee, The category of intuitionistic fuzzy topological spaces, Bull. Korean. Math. Soc. 37 (2000), 63-76.

  23. F. G. Lupianez, Quasicoincident for intuitionistic fuzzy points, Int. J. Math. Sci. 10 (2005), 1539-1542.

  24. F. Marty, Sur une generalization de la notion de groupe, 8 iem Congress Math. Scandinaves, Stockholm, (1934), 45-90.

  25. S. Padmapriya, M. K. Uma and E. Roja, A study on intuitionistic fuzzy topological groups, Ann. Fuzzy Math. Inform. 76 (2014), 991-1004.

  26. P. K. Sharma, (α,β)-cut of Intuitionistic fuzzy groups, International Mathematics Forum 6 (2011), 2605-2614.

  27. P. K. Sharma, t- Intuitionistic fuzzy subgroups, International Journal of Fuzzy Mathematics and Systems 3 (2012), 233-243.

  28. M.M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J. Fuzzy Math. 3 (1995), 1-15.