Category of Fuzzy Topological Polygroups

Article Sidebar

PDF
Cite as:
N. Abbasizadeh, B. Davvaz, Category of Fuzzy Topological Polygroups, Int. J. Anal. Appl., 11 (2) (2016), 124-136.

Main Article Content

N. Abbasizadeh, B. Davvaz

Abstract

In this paper, the relation between two definitions of a fuzzy topological polygroup is discussed. The collection of all fuzzy continuous functions from a fuzzy topological space Y to a fuzzy topological polygroup Z, denoted by FC(Y,Z) induces a polygroup structure from that of Z. Moreover, we study (fuzzy) topological polygroup of the polygroup FC(Y,Z) when it is equipped with various known topologies and fuzzy topologies. Also, a few properties of fuzzy topological polygroups are established and a category CFTP is formed with objects as FTP and morphisms as the fuzzy topological homomorphisms. The category CTP is seen to be a full subcategory of CFTP.

Article Details

References

  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. H. Aghabozorgi, B. Davvaz and M. Jafarpour, Solvable polygroups and drived subpolygroups, Comm. Algebra 41(8) (2013), 3098-3107.
  4. C.L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl 24 (1968), 182-190.
  5. I. Chon, Properties of fuzzy topological groups and semigroups, Kangweon-Kyungki Math. 8 (2000), 103-110.
  6. S. D. Comer, Polygroups derived from cogroups, J. Algebra 89 (1984), 397-405.
  7. P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.
  8. B. Davvaz and I. Cristea, Fuzzy Algebraic Hyperstructures-An Introduction, Springer, 2015.
  9. B. Davvaz, Polygroup Theory and Related System, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
  10. A. Deb Ray, On (Left) fuzzy topological ring, Int. Math. Forum 6(27) (2011), 1303-1312.
  11. A. Deb Ray, On fuzzy topological ring valued fuzzy continuous functions, Appl. Math. Sci. (Ruse) 3 (2009), 1177-1188.
  12. A. Deb Ray, P. Chettri and M. Sahu, More on left fuzzy topological rings, Annals of Fuzzy Mathematics and Informatics 3 (2012), 321-333.
  13. D.H. Foster, Fuzzy topological groups, J. Math. Anal. Appl. 67 (1979), 549-564.
  14. D. N. Georgiou, On fuzzy function spaces, J. Fuzzy Math. 9(1) (2001), 111-126.
  15. D. Heidari, B. Davvaz and S.M.S. Modarres, Topological hypergroups in the sense of Marty, Comm. Algebra 42 (2014), 4712-4721.
  16. D. Heidari, B. Davvaz and S.M.S. Modarres, Topological polygroups, Bull. Malays. Math. Sci. Soc. 39 (2016), 707-721.
  17. M. Jafarpour, H. Aghabozorgi and B. Davvaz, On nilpotent and solvable polygroups, Bulletin of Iranian Mathematical Society 39(3) (2013), 487-499.
  18. G. Jagar, On fuzzy function spaces, Internal J. Math. Math Sc. 22(4) (1999), 727-737.
  19. J.L. Ma and C.H Yu, Fuzzy topological groups, Fuzzy Sets and Systems 12 (1984), 289-299.
  20. F. Marty, Sur une generalization de la notion de groupe, 8iemCongress Math. Scandinaves, Stockholm (1934), 45-90.
  21. P.M. Pu and Y.M. Liu, Fuzzy topology 1, J. Math. Anal. Appl. 76 (1980), 571-599.
  22. P.M. Pu and Y.M. Liu, Fuzzy topology 2, J. Math. Anal. Appl. 77 (1980), 20-37.
  23. A. P. Shostak, Two decades of fuzzy topology: Basic ideas, notions and results, Russian Math. Surveys 44 (1989), 125-186.
  24. M.M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and fuzzy subpolygroups, J. Fuzzy Math. 3 (1995), 1-15.