A comparative study of soft sets with fuzzy sets and rough sets

This paper reviews some basic properties of fuzzy, rough and soft sets, and compares soft sets to the related concepts of fuzzy and rough sets. The definitions of soft set intersection and union are revised. The two are based on the Cartesian product of the sets of parameters. It illustrates that one could obtain other specific union and intersection by using some cutting operations to the Cartesian product. The definition of soft set complement is also revised. One is taken by a collection of sets instead of the previous rigid complement. By means of soft mapping proposed by Molodtsov, both fuzzy set and rough set may be considered as a special soft set with specific parameters and set-valued mapping. And then the basic operations of fuzzy and rough sets are reconsidered in the framework of soft sets. With the new insight into soft sets, their connections and differences between soft sets and fuzzy sets, soft sets and rough sets, are discussed.

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