On Fuzzy Ordered LA-Semihypergroups

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Muhammad Azar, Muhammad Gulistan, Naveed Yaqoob, Seifedine Kadry

Abstract

We introduce the notion of fuzzy ordered LA-semihypergroups and provide different examples. We also discuss some results related with fuzzy left and right hyperideals.

Article Details

References

  1. F. Marty, Sur uni generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934) 45-49.
  2. P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital. B., 1(2) (1982) 717-727.
  3. B. Davvaz, Some results on congruences in semihypergroups, Bull. Malyas. Math. Sci. So. 23 (2000) 53-58.
  4. D. Freni, Minimal order semihypergroups of type U on the right, II, J. Algebra, 340 (2011) 77-80.
  5. K. Hilla, B. Davvaz and K. Naka, On quasi-hyperideals in semihypergroups, Commun. Algebra, 39 (2011) 4183.
  6. V. Leoreanu, About the simplifiable cyclic semihypergroups, Italian J. Pure Appl. Math., 7 (2000) 69-76.
  7. M. D. Salvo, D. Freni and G. Lo Faro, Fully simple semihypergroups, J. Algebra, 399 (2014) 358-377.
  8. D. Heidari and B. Davvaz, On ordered hyperstructures, U. P. B. Sci. Bull. Series A, 73 (2011) 85-96.
  9. M. Bakhshi and R.A. Borzooei, Ordered polygroups, Ratio Math, 24 (2013) 31-40.
  10. J. Chvalina, Commutative hypergroups in the sense of Marty and ordered sets, in: Proc. Summer School, Gen. Algebra ordered Sets, Olomouc (Czech Republic), (1994) 19-30.
  11. S. Hoskova, Upper order hypergroups as a reflective subcategory of subquasiorder hypergroups, Ital. J. Pure Appl. Math., 20 (2006) 2015-222.
  12. M. Kondo and N. Lekkoksung, On intra-regular ordered Γ-semihypergroups, Int. J. Math. Anal., 7(28) (2013) 1379-1386.
  13. M. Novak, EL-hyperstructures, Ratio Math., 23 (2012) 65-80.
  14. K. Hila and J. Dine, On hyperideals on left almost semihypergroups, ISRN Algebra, (2011) Article ID 953124 8Pages.
  15. M. A. Kazim and M. Naseerudin, On almost semigroup, Aligarh Bull. Math., 2 (1972) 1-7.
  16. N. Yaqoob, P. Corsini and F. Yousafzai, On Intra-regular left almost semihypergroups with pure left identity, J. Math., Article ID 510790 (2013) 10 pages.
  17. N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc., 23(2) (2015) 231-235.
  18. L. A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965) 338-353.
  19. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971) 512-517.
  20. P. Corsini, M. Shabir and T. Mahmood, Semisimple semihypergroups in terms of hyperideals, Iran J. Fuzzy. Syst., 8 (2011) 95-111.
  21. P. Corsini, Fuzzy multiset hyperstructures, European J. Comb., 44 (2015) 198-207.
  22. B. Davvaz, Characterization of subsemihypergroups by various triangular norms, Czech. Math. J., 55(4) (2005) 923-932.
  23. B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure Appl. Math., 8 (200) 67-74.
  24. K. Hila and S. Abdullah, A study on intuitionistic fuzzy sets in Γ-semihypergroups, J. Intell. Fuzzy Syst., 26 (2014) 1695-1710.
  25. A. Khan, M. Farooq, M. Izhar and B. Davvaz, Fuzzy hyperideals of left almost semihypergroups, Int. J. Anal. Appl., 15(2) (2017) 155-171.
  26. B. Pibaljommee, K. Wannatong and B. Davvaz, An investigation on fuzzy hyperideals in ordered in semihypergroups, Quasigroups and Relat. Syst., 23 (2015) 297-308.
  27. B. Pibaljommee and B. Davvaz, Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups, J. Intell. Fuzzy Syst., 28 (2015) 2141-2148.
  28. J. Tang, A. Khan and Y. Luo, Characterizations of semisimple ordered semihypergroups in term of fuzzy hyperideals, J. Intell. Fuzzy Syst., 30(3) (2016) 1735-1753.
  29. J. Tang, B. Davvaz and X. Xie, A study on (fuzzy) quasi-Γ-hyperideals in ordered Γ-semihypergroups, J. Intell. Fuzzy Syst., 32(6) (2017) 3821-3838.
  30. J. Tang, B. Davvaz and Y. Luo, A study on fuzzy hyperideals in ordered semihypergroups, Italian J. Pure Appl. Math., 36 (2016) 125-146.
  31. J. Tang, B. Davvaz and Y.F. Luo, Hyperfilters and fuzzy hyperfilters of ordered semihypergroups, J. Intell. Fuzzy Syst., 29(1) (2015) 75-84.
  32. N. Tipachot and B. Pibaljommee, Fuzzy interior hyperideasl in ordered semihypergroups, Italian J. Pure Appl. Math., 36 (2016) 859-870.
  33. J. Zhan and B. Davvaz, Study of fuzzy algebraic hypersystems from a general view point, Int. J. Fuzzy Syst., 12 (2010) 73-79.
  34. J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hypernear-rings, Inform Sci., 178 (2008) 425-438.