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...

1.1. Strictly Cyclic Modules and Modular Right Ideals. For a ring A with identity, cyclic modules are precisely those of the form a\A where a is a right ideal. What might be a useful analogous statement for a ring without identity? This question motivates what follows in this subsection. A module M is strictly cyclic if there exists m in M such that mA = M (such an m is called a generator); a r...

By means of soft intersection-union sum and product, we make a new approach to the hemiring theory via soft set theory with the concepts of soft union (h-ideals, h-bi-ideals, h-quasi-ideals and h-interior ideals). Also, we investigate some characteristics of h-semisimple and h-quasihemiregular hemirings using these kinds of soft union h-ideals. 2000 AMS Classification: 16Y60; 13E05.

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semig...

In this paper, the notions of left-right (resp. right-left) t-derivations of BCC-algebras are studied and some properties on t-derivations of BCC-algebras are investigated. This paper also considers t-regular t -derivations and the dt-invariant on ideals of BCC-algebras. Mathematics Subject Classification: 06F35

In this paper basic notions of rough intuitionistic fuzzy set in semigroups are given and we discuss some of its basic properties. We introduce the notions of rough intuitionistic fuzzy left (right, two-sided, bi-, (1, 2)-) ideals in a semigroup and give some properties of such ideals.

Our aim in this paper is to introduce and study a new sort of fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal) of a ternary semigroup, called interval-valued (α,β )-fuzzy ternary subsemigroup (left ideal, right ideal, lateral ideal, quasi-ideal, bi-ideal). We also characterize regular ternary semigroups in terms of these interval-valued fuzzy ideals.

We introduce and use the concept of (∈γ ,∈γ ∨qδ)-fuzzy (left, right, bi-) ideals to study the structural properties of a non-associative algebraic ordered structure. We characterize an intra-regular ordered AGgroupoid by these generalized fuzzy ideals. 2010 AMS Classification: 06F05, 20M12, 08A72

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...