m-Polar Fuzzy Hyperideals in LA-Semihypergroups

Elmoasry, Ahmed; Yaqoob, Naveed

doi:10.28924/2291-8639-17-2019-329

Research Article

m-Polar Fuzzy Hyperideals in LA-Semihypergroups

Ahmed Elmoasry¹
Naveed Yaqoob¹*

Majmaah University

* Corresponding author

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.

How to Cite

A. Elmoasry, N. Yaqoob, m-Polar Fuzzy Hyperideals in LA-Semihypergroups, Int. J. Anal. Appl. 17 (2019), 329–341. https://doi.org/10.28924/2291-8639-17-2019-329

BibTeX

@article{Elmoasry2019,
  author  = {Elmoasry, Ahmed and Yaqoob, Naveed},
  title   = {m-Polar Fuzzy Hyperideals in LA-Semihypergroups},
  journal = {Int. J. Anal. Appl.},
  volume  = {17},
  year    = {2019},
  pages   = {329--341},
  doi     = {10.28924/2291-8639-17-2019-329}
}

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.