By means of a kind of new idea, we redefine some kinds of fuzzy ideals in a ring and investigate some of their related properties. The concepts of strong prime (semiprime) generalized fuzzy (bi-, quasi-) ideals in rings are introduced. In particular, we discuss the relationships between strong prime (resp., semiprime) generalized fuzzy (bi-, quasi-) ideals and prime (resp. semiprime) generalize...

In any semigroup S, we say that elements a and b are left inverses of each other if a = aba, b = bab and a L b, in which case we write a γ b. Right inverses are defined dually with the notation δ. Set τ = δγ. We study the classes of semigroups in which τ has some of the usual properties of a relation. We also consider properties of (maximal) completely simple subsemigroups of S. In terms of the...

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semig...