In this paper, we introduce the concept of (α, β)-fuzzy ideals in ternary semigroups, which is a generalization of fuzzy ideals in ternary semigroups. We investigate the related properties of ternary semigroups. The lower and upper parts of fuzzy subsets of a ternary semigroup are defined. Characterizations of regular ternary semigroups by the properties of the lower part of (∈,∈∨q)-fuzzy left ...

A characterization of an h-hemiregular hemiring in terms of a fuzzy h-ideal is provided. Some properties of prime fuzzy h-ideals of h-hemiregular hemirings are investigated. It is proved that a fuzzy subset f of a hemiring S is a prime fuzzy left (right) h-ideal of S if and only if f is two-valued, f(0) = 1, and the set of all x in S such that f(x) = 1 is a prime (left) right h-ideal of S. Fina...

olds ( α̃, β̃ ) and interval valued fuzzy generalized bi-ideals with thresholds ( α̃, β̃ ) , which are generalization of interval valued fuzzy ideals, interval valued fuzzy interior ideals, interval valued fuzzy quasi ideals and interval valued fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. Characterizations of regular semigroups by the properti...

In the theory of rings, the properties of derivations are important. In [15], Jun and Xin applied the notion of derivations in ring and near-ring theory to BCI-algebras, and they also introduced a new concept called a regular derivation in BCI-algebras. They investigated some properties of its .In this manuscript, the concept of fuzzy left (right) derivations BCCideals in BCC-algebras is introd...

In this paper we introduce bipolar fuzzy subsemigroup, bipolar fuzzy left (right) ideals and bipolar fuzzy bi-ideal in ordered semigroups. We characterize different classes of ordered semigroups by the properties of their bipolar fuzzy ideals and bipolar fuzzy bi-ideals.

In this paper, soft intersection LA-semigroups, soft intersection left (right, two-sided) ideals, (generalized) bi-ideals, interior ideals, quasi-ideals in LA-semigroups are defined, their examples and properties are given and their interrelations are obtained.

Most of the results on semigroups or ordered can be transferred to hypersemigroups hypersemigroups, respectively. The same, if we replace word "semigroup" by "groupoid", "hypersemigroup" "hypergroupoid". We show way pass from fuzzy hypersemigroups.

The concepts of ∈-soft sets and q-soft sets in AG-groupoids are introduced and some related properties are investigated. In particular, we describe the relationships among ordinary fuzzy interior ideals and soft interior ideals over an AG-groupoid S. Moreover, we study the relation-ships among (∈, ∈ ∨q)fuzzy interior ideals, ( ) , q ∈∈∨ -fuzzy interior ideals, (α; β)-fuzzy interior ideals and s...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

In this paper, we first introduce the new concept of completely semiprime fuzzy ideals of an ordered semigroup S, which is an extension of completely semiprime ideals of ordered semigroup S, and investigate some its related properties. Especially, we characterize an ordered semigroup that is a semilattice of simple ordered semigroups in terms of completely semiprime fuzzy ideals of ordered semi...