Study Of Soft Set Theory, Its Algebra And Application

ABSTRACT

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.