Title: On Fuzzy Ordered LA-Semihypergroups
Author(s): Muhammad Azar, Muhammad Gulistan, Naveed Yaqoob, Seifedine Kadry
Pages: 276-289
Cite as:
Muhammad Azar, Muhammad Gulistan, Naveed Yaqoob, Seifedine Kadry, On Fuzzy Ordered LA-Semihypergroups, Int. J. Anal. Appl., 16 (2) (2018), 276-289.


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.

Full Text: PDF



  1. F. Marty, Sur uni generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934) 45-49. Google Scholar

  2. P. Bonansinga and P. Corsini, On semihypergroup and hypergroup homomorphisms, Boll. Un. Mat. Ital. B., 1(2) (1982) 717-727. Google Scholar

  3. B. Davvaz, Some results on congruences in semihypergroups, Bull. Malyas. Math. Sci. So. 23 (2000) 53-58. Google Scholar

  4. D. Freni, Minimal order semihypergroups of type U on the right, II, J. Algebra, 340 (2011) 77-80. Google Scholar

  5. K. Hilla, B. Davvaz and K. Naka, On quasi-hyperideals in semihypergroups, Commun. Algebra, 39 (2011) 4183. Google Scholar

  6. V. Leoreanu, About the simplifiable cyclic semihypergroups, Italian J. Pure Appl. Math., 7 (2000) 69-76. Google Scholar

  7. M. D. Salvo, D. Freni and G. Lo Faro, Fully simple semihypergroups, J. Algebra, 399 (2014) 358-377. Google Scholar

  8. D. Heidari and B. Davvaz, On ordered hyperstructures, U. P. B. Sci. Bull. Series A, 73 (2011) 85-96. Google Scholar

  9. M. Bakhshi and R.A. Borzooei, Ordered polygroups, Ratio Math, 24 (2013) 31-40. Google Scholar

  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. Google Scholar

  11. S. Hoskova, Upper order hypergroups as a reflective subcategory of subquasiorder hypergroups, Ital. J. Pure Appl. Math., 20 (2006) 2015-222. Google Scholar

  12. M. Kondo and N. Lekkoksung, On intra-regular ordered Γ-semihypergroups, Int. J. Math. Anal., 7(28) (2013) 1379-1386. Google Scholar

  13. M. Novak, EL-hyperstructures, Ratio Math., 23 (2012) 65-80. Google Scholar

  14. K. Hila and J. Dine, On hyperideals on left almost semihypergroups, ISRN Algebra, (2011) Article ID 953124 8Pages. Google Scholar

  15. M. A. Kazim and M. Naseerudin, On almost semigroup, Aligarh Bull. Math., 2 (1972) 1-7. Google Scholar

  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. Google Scholar

  17. N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc., 23(2) (2015) 231-235. Google Scholar

  18. L. A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965) 338-353. Google Scholar

  19. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971) 512-517. Google Scholar

  20. P. Corsini, M. Shabir and T. Mahmood, Semisimple semihypergroups in terms of hyperideals, Iran J. Fuzzy. Syst., 8 (2011) 95-111. Google Scholar

  21. P. Corsini, Fuzzy multiset hyperstructures, European J. Comb., 44 (2015) 198-207. Google Scholar

  22. B. Davvaz, Characterization of subsemihypergroups by various triangular norms, Czech. Math. J., 55(4) (2005) 923-932. Google Scholar

  23. B. Davvaz, Fuzzy hyperideals in semihypergroups, Italian J. Pure Appl. Math., 8 (200) 67-74. Google Scholar

  24. K. Hila and S. Abdullah, A study on intuitionistic fuzzy sets in Γ-semihypergroups, J. Intell. Fuzzy Syst., 26 (2014) 1695-1710. Google Scholar

  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. Google Scholar

  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. Google Scholar

  27. B. Pibaljommee and B. Davvaz, Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups, J. Intell. Fuzzy Syst., 28 (2015) 2141-2148. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  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. Google Scholar

  32. N. Tipachot and B. Pibaljommee, Fuzzy interior hyperideasl in ordered semihypergroups, Italian J. Pure Appl. Math., 36 (2016) 859-870. Google Scholar

  33. J. Zhan and B. Davvaz, Study of fuzzy algebraic hypersystems from a general view point, Int. J. Fuzzy Syst., 12 (2010) 73-79. Google Scholar

  34. J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hypernear-rings, Inform Sci., 178 (2008) 425-438. Google Scholar


Copyright © 2020 IJAA, unless otherwise stated.