On weakly bi-ideals in ordered semigroups and their fuzzifications

Abstract

The concept of bi-ideals in ordered semigroups is a subuniverse of ordered semigroups with certain conditions. It can be used to characterize ordered semigroups. In this paper, we extend the concept of bi-ideals to a general way, so-called weakly biideals. We consider the primitive and semiprimitive of weakly bi-ideals. Some connections between prime (semiprime) weakly bi-ideals and fuzzy prime (semiprime) weakly bi-ideals is established.