Volume 35 • Number 4 • 2012   • Characterization of Ordered Semigroups in Terms of Fuzzy Soft Ideals Yunqiang Yin and Jianming Zhan Abstract. 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. 2010 Mathematics Subject Classification: 20M12, 08A72. Full text: PDF