Conveying group theory to soft uni-groups

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. This theory has been applied to many fields such as information systems, decision making problems, optimization theory, algebraic structures and basic mathematics analysis, etc. which contain uncertainties. In this thesis, we define soft product on a soft set the parameter of which is the elements of a group and derive its basic properties. We proof some theorems releated to Normal Soft Uni-Groups and investigate its relation as regards soft product which we defined. We demonstrate that soft images of functions are preserved under the homomorphic structure in Soft Uni-Groups. The soft characteristic function is defined and its properties are shown. We also construct soft coset and quotient groups with the soft product operation in the A-α soft set.