Abstract: The aim of this paper is to introduce the concepts of (∈, ∈∨q)-fuzzy subalgebras, (∈,∈∨q)-fuzzy ideals and (∈,∈∨q)-fuzzy quotient algebras of BCI-algebras with operators, and to investigate their basic properties.
Abstract: The notions of prime(semiprime) fuzzy h-ideal(h-biideal,
h-quasi-ideal) in Γ-hemiring are introduced and some of their
characterizations are obtained by using "belongingness(∈)" and
"quasi - coincidence(q)". Cartesian product of prime(semiprime)
fuzzy h-ideals of Γ-hemirings are also investigated.
Abstract: Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈,∈ ∨q)-fuzzy ideals, (∈,∈ ∨q)-fuzzy bi-ideals and (∈,∈ ∨q)-fuzzy generalized bi-ideals of an ordered semigroup S, and investigate their related properties. Furthermore, we also define the upper and lower parts of fuzzy subsets of an ordered semigroup S, and investigate the properties of (∈,∈ ∨q)-fuzzy ideals of S. Finally, characterizations of regular ordered semigroups and intra-regular ordered semigroups by means of the lower part of (∈ ,∈ ∨q)-fuzzy left ideals, (∈,∈ ∨q)-fuzzy right ideals and (∈,∈ ∨q)- fuzzy (generalized) bi-ideals are given.
Abstract: The purpose of this note is to obtain some properties of
(∈,∈ ∨q)- fuzzy bi-ideals in a Γ-semigroup in order to characterize
regular and intra-regular Γ-semigroups.