STUDY OF SOFT SET THEORY, ITS ALGEBRA AND APPLICATION

This dissertation presents a systematic and critical study of the fundamenta.lli of soft set theory which includes soft set operations, soft set relations and functions, soft matrices and their properties. In course of studying operations on soft sets, the complementation operation is strengthened, some new results on distributive and absorption properties with respect to various soft set operations are obtained,and soft set operations and their corresponding soft matrix operations are shown to be equivalent. An up-to-date study of soft algebraic structures such as soft groups, softrings, soft semirings and soft lattices is presented. In particular,new concepts are introduced, which helped developing certai:i monoids, semirings and lattices of soft subsets and partitions of a soft set with respect to various operations on soft sets. Finally techniques of applications of soft set theory in decision making are investigated and exemplified. It was observed that Soft Choice Matrix technique can solve problems involving a huge number of decision makers in a much economical way.