Geodesic
Characterization of Ordered Semigroups in Terms of Fuzzy Soft Ideals
Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4
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In this paper, we apply the concept of fuzzy soft sets to ordered semigroup theory. The concepts of $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy left (right) ideals, $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy bi-ideals and $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy soft left (right) ideals of an ordered semigroup are derived. The characterization of left quasi-regular ordered semigroups and ordered semigroups that are left quasi-regular and intra-regular in terms of $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy left (right) ideals, $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy bi-ideals and $(\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})$-fuzzy quasi-ideals is discussed.
Classification : 20M12, 08A72. 
@article{BMMS_2012_35_4_a15,
     author = {Yunqiang Yin and Jianming Zhan},
     title = {Characterization of  {Ordered} {Semigroups} in {Terms} of {Fuzzy} {Soft} {Ideals}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2012},
     volume = {35},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a15/}
}
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Yunqiang Yin; Jianming Zhan. Characterization of  Ordered Semigroups in Terms of Fuzzy Soft Ideals. Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2012_35_4_a15/