In this article, we present and rigorously analyze the notion of soft polyaction, providing a detailed framework together with several fundamental characterizations of this newly introduced concept. Beyond the introductory formulation, we further develop the associated structures by defining and examining the notions of stabilizer, normalizer, and centralizer within the context of soft polyactions. Particular attention is devoted to clarifying the intricate interrelations among these structures, and we supply explicit examples that illustrate their behavior and highlight their relevance. A central objective of this study is to extend the algebraic machinery of group theory into the broader setting of hyperstructures. To this end, we investigate the semi-direct product of soft polygroups and establish an analogue of Cayley’s theorem for such objects. These developments naturally culminate in the formulation of soft crossed polymodules, which provide a unifying perspective and serve as a bridge between traditional group-theoretic constructions and the more general theory of algebraic hyperstructures. The proposed framework not only broadens the scope of classical algebraic results but also clarifies methodological pathways for future research. By introducing the notion of soft crossed polymodules, we demonstrate how researchers can systematically extend well-established concepts from group theory to the rich and increasingly significant domain of soft algebraic hyperstructures.
Mohammad Dehghanizadeh (2025) studied this question.