In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part of various problems. We also characterize a weakly regular class of an AG***-groupoid by using generated ideals and soft intersection ideals. We investigate the relationship between SI-left-ideal, SI-right-ideal, SI-two-sided-ideal, and SI-interior-ideal of an AG-groupoid over a universe set by providing some practical examples.

中文翻译：

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基于理想理论的 AG-groupoid 软集理论方法与应用

在本文中，我们使用软集理论研究了称为 AG-groupoid 的非关联代数结构的结构特性。我们根据软相交理想刻画了一个正确的 AG-groupoid 类，并提供了反例来讨论各种问题的逆向部分。我们还通过使用生成的理想和软相交理想来表征 AG***-groupoid 的弱正则类。我们通过提供一些实际示例来研究 AG-groupoid 在宇宙集上的 SI-left-ideal、SI-right-ideal、SI-two-side-ideal 和 SI-interior-ideal 之间的关系。