Characterization of Ordered Semigroups in Terms of Fuzzy Soft Ideals

Yunqiang Yin ; Jianming Zhan

Bulletin of the Malaysian Mathematical Society, Tome 35 (2012) no. 4

Résumé

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.

Détail

Classification : 20M12, 08A72.