A new approach to soft groups based on soft binary operations

In this paper, we propose a new definition for soft groups based on soft binary operations. The idea is to bring the archetype of "softness" into the spectrum of algebraic structures using soft binary operations parametrized by a given set of suitable parameters. One of our achievement is that we obtain an ordinary group model representing our soft group. The existing classical group serves as a model to describe and characterize the overall internal properties of our soft groups. In this vein, we further investigate the soft subgroups (respectively, normal soft subgroups) and proved some structural theorems.