A novel approach to AG-groupoids via soft intersection product operation

This study investigates some general properties of soft sets on a symmetry-preserving structure AG-groupoid. Various weaknesses in the papers Karaaslan [22] and Sezgin [39] are rectified, and some generalizations and simplifications. Also, it is investigated that the family of soft sets over AG-groupoid is again an AG-groupoid when equipped with the soft intersection-product (SI-product) operation. Moreover, it is proven that the family of soft sets over an AG-groupoid possesses the properties of being medial, paramedial, Bol*, and nuclear square under the SI-product operation.The application of the soft set theory, specifically the SI-product, is extended to AG-groupoids. Some properties of left abelian distributive (LAD) AG-groupoids (LAD-AG-groupoids) and right abelian distributive (RAD) AG-groupoids (RAD-AG-groupoids) under the SI-product of soft sets are investigated. Counterexamples to show that the family of soft sets on a set S (S(S)) is not soft intersection-left abelian distributive (SI-LAD) and soft intersection-right abelian distributive (SIRAD) are given. Also, the conditions under which they become SI-LAD and SI-RAD are investigated. Some of the examples in this article were obtained using modern techniques such as Mace4 and Prover9.