Study On The Type-2 Soft Set Extensions And Applications

Soft set is a tool to deal with uncertainty problems,which is a hotspot of research in economy,military,management,mathematics,and engineering at present.Regarding the limitation of soft set in dealing with decision problems,this thesis puts forward the model of Type-2 soft set.Type-2 soft set is the extension of soft set concept.The thesis studies the algorithm and property of Type-2 soft set.At the same time,it puts forward the theory of Type-2 weighted soft set,and applies Type-2weighted soft set and its property to solve decision problems.The major work of this thesis includes:(1)According to the soft set theory,it proposes Type-2 soft set and defines its basic concept,and then explains the concept of Type-2 soft set with examples.According to the relationship between soft set and fuzzy set,the thesis studies Type-2soft set and Type-2 fuzzy set,and then proves that Type-2 fuzzy set is a special Type-2 soft set.(2)It defines the algorithm of Type-2 soft set.It proves the theorem and property of Type-2 soft set,according to the relevant property of Type-1 soft s et and the definition of Type-2 soft set.Through the research on soft set's measurement of uncertainty,it is expanded to Type-2 soft set.(3)The thesis puts forth Type-2 weighted soft set and applies it to decision-making.It contrasts Type-2 soft set with Type-1 soft set and thus proves the superiority of Type-2 soft set.