Abstract
In this paper we have defined anti fuzzy interior ideal in semigroups. We characterize regular, intra-regular and left (right) quasi-regular semigroups by the properties of their anti fuzzy ideals, anti fuzzy bi-ideals, anti fuzzy generalized bi-ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals.
Highlights
The fundamental concept of a fuzzy set was first introduced by L
In this paper, which is the continuation of the work carried out by M
It is easy to prove that S is left quasi-regular if and only if a ∈ S aS a (a ∈ aS aS ), this implies that there exist elements x, y ∈ S such that a = xaya (a = axay)
Summary
The fundamental concept of a fuzzy set was first introduced by L. A fuzzy subset f of a semigroup S is called anti fuzzy left(right) ideal of S if f (xy) ≤ f (y) ( f (xy) ≤ f (x)) for all x, y ∈ S . A fuzzy subset f of a semigroup S is an anti fuzzy left(right) ideal of S if and only if Θ ∗ f ⊇ f ( f ∗ Θ ⊇ f ).
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