On Weakly Prime and Weakly Quasi-Prime Fuzzy Left Ideals in Ordered Semigroups
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On Weakly Prime and Weakly Quasi-Prime Fuzzy Left Ideals in Ordered Semigroups

Authors: Jian Tang

Abstract:

In this paper, we first introduce the concepts of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S. Furthermore, we give some characterizations of weakly prime and weakly quasi-prime fuzzy left ideals of an ordered semigroup S by the ordered fuzzy points and fuzzy subsets of S.

Keywords: Ordered semigroup, ordered fuzzy point, weakly prime fuzzy left ideal, weakly quasi-prime fuzzy left ideal.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1331749

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[1] N. Kehayopulu and M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum, 65(2002), 128-132.
[2] N. Kehayopulu and M. Tsingelis, The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets, Information Sciences, 152(2003), 231-236.
[3] X. Y. Xie and J. Tang, Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Information Sciences, 178(2008), 4357-4374.
[4] X. Y. Xie, J. Tang and F. Yan, A characterization of prime fuzzy ideals of ordered semigroups, Fuzzy Systems and Mathematics, 22(2008), 39-44.
[5] X. Y. Xie and J. Tang, Regular ordered semigroups and intra-regular ordered semigroups in terms of fuzzy subsets, Iranian Journal of Fuzzy Systems, 7(2)(2010), 121-140.
[6] A. Khan, M. Shabir and Y. B. Jun, Intuitionistic fuzzy quasi-ideals of ordered semigroups, Russian Mathematics (Iz. VUZ), 54(12)2010, 59- 71.
[7] M. Shabir and A. Khan, Characterizations of ordered semigroups by the properties of their fuzzy ideals, Comput. Math. Appl., 59(1)(2010), 539- 549.
[8] B. Davvaz and A. Khan, Characterizations of regular ordered semigroups in terms of (╬▒, β)-fuzzy generalized bi-ideals, Information Sciences, 181(2011), 1759-1770.
[9] N.Kehayopulu and M.Tsingelis, On weakly prime ideals of ordered semigroups, Math. Japonica, 35(6)(1990), 1051-1056.
[10] X. Y. Xie and M. F. Wu, On quasi-prime, weakly quasi-prime left ideals in ordered semigroups, PU.M.A (Hungary), 6(1995), 105-120.
[11] J. Tang and X. Y. Xie, Some characterizations of strongly semisimple ordered semigroups, Advances in Mathematics, (to appear)
[12] J. Tang, On completely semiprime, semiprime and prime fuzzy ideals in ordered semigroups, International Journal of Engineering and Natural Sciences 5(1) (2011), 35-40.
[13] J. Tang, Chains of archimedean ordered semigroups by terms of fuzzy subsets, World Academy of Science, Engineering and Technology 80 (2011), 957-963.
[14] X. Y. Xie, An introduction to ordered semigroup theory. Beijing: Kexue Press, 2001.
[15] X. Y. Xie and M. F. Wu, The Theory of Fuzzy Semigroups. Beijing: Kexue Press, 2005.