m-Polar Fuzzy Hyperideals in LA-Semihypergroups

Article Sidebar

PDF
Cite as:
Ahmed Elmoasry, Naveed Yaqoob, m-Polar Fuzzy Hyperideals in LA-Semihypergroups, Int. J. Anal. Appl., 17 (3) (2019), 329-341.

Main Article Content

Ahmed Elmoasry, Naveed Yaqoob

Abstract

In this paper, we initiate a study of m-polar fuzzy sets in hyperstructure theory, particularly in left almost semihypergroups. We define an m-polar fuzzy left (right, two sided) hyperideal in a left almost semihypergroup and provided some results on these m-polar fuzzy left (right, two sided) hyperideals.

Article Details

References

  1. F. Marty, Sur une generalization de la notion de group, 8th Congres Math. Scandinaves, Stockholm, (1934), 45-49.
  2. P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, (1993).
  3. T. Vougiouklis, Hyperstructures and their representations, Hadronic Press, Florida, (1994).
  4. B. Davvaz, Semihypergroup Theory. Elsevier /Academic Press, London, 2016.
  5. K. Hila and J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra, 2011 (2011), Article ID 953124.
  6. N. Yaqoob, P. Corsini and F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math. 2013 (2013), Art. ID 510790.
  7. F. Yousafzai, P. Corsini, Some charactrization problems in LA-semihypergroups, J. Algebra Number Theory, Adv. Appl. 10(1-2) (2013), 41-55.
  8. V. Amjad, K. Hila, F. Yousafzai, Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 20 (2014), 1063-1076.
  9. F. Yousafzai, K. Hila, P. Corsini, A. Zeb, Existence of non-associative algebraic hyper-structures and related problems, Afr. Mat. 26(5) (2015), 981-995.
  10. L. A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965), 338-353.
  11. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517.
  12. J. M. Anthony and H. Sherwood, Fuzzy subgroups redefined, J. Math. Anal. Appl., 69 (1979), 124-130.
  13. H. Sherwood, Products of fuzzy subgroups, Fuzzy Sets Syst. 11 (1983), 79-89.
  14. M. Asaad, Groups and fuzzy subgroups, Fuzzy Sets Syst. 39 (1991), 323-328.
  15. N. P. Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Inform. Sci. 34 (1984), 225-239.
  16. P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981), 264-269.
  17. B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure Appl. Math. 8 (2000), 67-74.
  18. B. Davvaz, I. Cristea, Fuzzy algebraic hyperstructures. An introduction. Studies in Fuzziness and Soft Computing, Springer, (2015).
  19. W. R. Zhang, Bipolar fuzzy sets, Proc. FUZZ-IEEE, (1998), 835-840.
  20. J. Chen, S.-G. Li, S. Ma and X. W, m-polar fuzzy sets: An extension of m-polar fuzzy sets, Sci. World J. 2014 (2014), Art. ID 416530.
  21. M. Akram and A. Farooq, m-polar fuzzy Lie ideals of Lie algebras, Quasigroups Relat. Syst. 24(2) (2016), 141-150.
  22. M. Akram, A. Farooq and K. P. Shum, On m-polar fuzzy Lie subalgebras, Italian J. Pure Appl. Math. 36 (2016) 445-454
  23. M. Akram and N. Waseem, Certain metrics in m-polar fuzzy graphs, New Math. Nat. Comput. 12(2) (2016), 135-155.
  24. M. Akram and H. R. Younas, Certain types of irregular m-polar fuzzy graphs, J. Appl. Math. Comput. 53(1-2) (2017), 365-382.
  25. A. Farooq, G. Ali and M. Akram, On m-polar fuzzy groups, Int. J. Algebra Stat. 5(2) (2016), 115-127.
  26. M. Sarwar and M. Akram, Novel applications of m-polar fuzzy concept lattice, New Math. Nat. Comput. 13(3) (2017), 261-287.
  27. M. Sarwar and M. Akram, New applications of m-polar fuzzy matroids, Symmetry, 9(12) (2017), Art. ID 319.
  28. M. Akram, m-polar fuzzy graphs, Studies in Fuzziness and Soft Computing, vol 371, Springer, (2019).
  29. A. Al-Masarwah and A. G. Ahmad, m-polar (α, β)-fuzzy ideals in BCK/BCI-algebras, Symmetry, 11 (2019), Art. ID 44.