On Actions of Soft Digroups

Soft set theory has emerged as a powerful mathematical framework for modeling uncertainty, imprecision, and vagueness, making it a valuable tool in both pure and applied mathematics. It has been extensively studied within algebraic structures, which are fundamental mathematical systems playing a central role in abstract algebra. This study introduces soft digroups through the combination of soft set theory with digroups, which are a generalisation of groups with two operations. Some characterizations of soft digroups are established and several examples are given to illustrate. Also, the actions of soft digroups are defined and a similar approach to Cayley’s theorem for soft digroups is presented.