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