Berhanu Bekele (PhD)Tesfaye Degife2025-08-172025-08-172025-06-18https://etd.aau.edu.et/handle/123456789/6846In this thesis, we propose a new de nition 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. In this thesis, we also study soft homomorphisms on soft groups and investigate their properties. Given a soft mapping hf;Ai from G to G0, we obtain an ordinary map ^f from the set SEA(G) of soft elements of G to the set SEA(G0) of soft elements of G0, and show that hf;Ai is a soft homomorphism (respectively, soft isomorphism) if and only if ^f is an ordinary group homomorphism (respectively, isomorphism). We apply this concept to study soft isomorphism theorems on soft groups. In addition, we study those soft automorphisms of soft groups and the particular class of soft inner automorphisms. Moreover, we study a few soft group-related ndings based on soft binary operations, including soft orbits, soft stabilizers, and the action of a soft group on a set. Given a soft mapping h ;Ai from G X to X; we obtain an ordinary map b from the set SEA(G) SEA(X) to the set SEA(X) and show that h ;Ai is a soft action if and only if b is an ordinary action. Finally, we present the fundamental ideas and characteristics of normal fuzzy soft subgroups.en-USStudy of Soft GroupsBased on Soft BinaryOperationsThesis