MORE GENERAL FORMS OF $(\alpha, \beta )$-FUZZY IDEALS OF ORDERED SEMIGROUPS

This paper consider the general forms of $(\alpha,\beta)$-fuzzy left ideals (right ideals, bi-ideals, interior ideals) of an ordered semigroup, where $\alpha,\beta\in\{\in_{\gamma},q_{\delta},\in_{\gamma}\wedge q_{\delta}, \in_{\gamma}\vee q_{\delta}\}$ and $\alpha\neq \in_{\gamma}\wedge q_{\delta}$. Special attention is paid to $(\in_{\gamma},\ivq)$-left ideals (right ideals, bi-ideals, interior ideals) and some related properties are investigated. The characterization of regular ordered semigroups in terms of $(\in_{\gamma},\ivq)$-fuzzy left (right) ideals, $(\in_{\gamma},\ivq)$-fuzzy bi-ideals and $(\in_{\gamma},\ivq)$-fuzzy interior ideals is also investigated.