Left regular $${\mathcal{AG}}$$ -groupoids in terms of fuzzy interior ideals

Abstract

The left and right regular classes of a semigroup theory plays essential role in studying the structural properties of the associative algebraic structure. In this paper, we show that these two classes coincides in an \({\mathcal{AG}}\)-groupoid with left identity which is a non-associative algebraic structure. As an application of our results we get characterizations of a left regular \({\mathcal{AG}}\)-groupoid in terms of fuzzy interior ideals and study some important properties in different aspects. Further we introduce a very basic theory for an \({\mathcal{AG}}\)-groupoid in terms of classical and fuzzy (left, right, two-sided, interior) ideals and show that how similar is the theory of an \({\mathcal{AG}}\)-groupoid with the theory of fuzzy \({\mathcal{AG}}\)-groupoid.