Generalized fuzzy ideals in ordered semirings

Abstract

In this paper, we introduce the concepts of $(\in ,\in \vee ({\kappa }^{\ast },q_{\kappa }))$-fuzzy left (right) ideals and $(\in ,\in \vee ({\kappa }^{\ast },q_{\kappa }))$-fuzzy ideals in ordered semirings. Some correspondence between (left, right) ideals and $(\in ,\in \vee ({\kappa }^{\ast },q_{\kappa }))$-fuzzy (left, right) ideals of ordered semirings are presented. Moreover, the notion of $({\kappa }^{\ast },\kappa )$-lower part of $(\in ,\in \vee ({\kappa }^{\ast },q_{\kappa }))$-fuzzy (left, right) ideals is defined and characterizations of different classes of ordered semirings are given.