Some Results on the Soft HG-Hypergroupoids

Abstract

Within the broader landscape of hyperstructure theory, a particular class of algebraic systems known as hypergroup-hypergroupoids emerges as a subject of significant mathematical interest. The present work is devoted to an in-depth exploration of this class, with special focus on its soft analog, namely, the Soft Hypergroup-Hypergroupoid (SHGD). The core objective of this study is to articulate and refine the conceptual and structural underpinnings of such systems, extending foundational principles derived from the well-established theories of soft hypergroups and soft hypergroupoids. By carefully developing this framework, we aim to uncover the layered interconnections, algebraic behavior, and underlying logic that govern these complex entities. Ultimately, this investigation aspires to broaden the theoretical horizons of soft algebraic structures, offering fresh perspectives and contributing meaningfully to the evolving discourse within hyperstructure-based mathematics.