Abstract
In this note, the authors introduce the notion of soft sets (briefly, S-sets) in an ordered -groupoid. We define and give some examples of SI-l-ideals, SI-r-ideals, and SI -bi-ideals in an ordered -groupoid and also investigate the relationship between them. We give an alternate definition for a strongly regular element of a unitary ordered -groupoid and show that how a strongly regular ordered -groupoid becomes an ordered -groupoid and a completely inverse ordered -groupoid. As an application, we get characterizations of a strongly regular ordered -groupoid in terms of SI-one-sided (two-sided) ideals and SI-bi-ideals via semilattices. Finally, we give the concept of an ordered -groupoid and give an example to show that this class is the generalization of a unitary ordered -groupoid.
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