The relation between fuzzy soft set and integrative fuzzy set

Abstract

Fuzzy set can be divided into single parameter or multi-parameter's ones with which to depict their fuzzy attributes. In references, it is usual defined in a single parameter universe and yet multi-parameter's ones often appears in so-called fuzzy relation. Fuzzy soft set can be used to describe a fuzzy object by aggregating fuzzy parameters in different attributes. Fuzzy set can be employed to do the same things. It can be concluded that there must be a certain relation between the two concepts. And to give the relation, integrative fuzzy set is proposed in this paper. And which can be decomposed into a fuzzy soft set under certain condition. Fuzzy soft set also can be translated into an integrative fuzzy set by some operator. Both of them can be used for decision-making. Theoretical analysis and examples show the optimal decision-making results are equivalent.