Fuzzy set-valued information systems and their homomorphisms based on data compression

A fuzzy set-valued information system (FSVIS) is a special information system (IS) where the value of an object under each attribute or each attribute value is a fuzzy set. Homomorphism is a powerful mathematical tool to deal with FSVISs, which can be used to study relationships among them. Based on data compression, we obtain some characterizations about FSVISs and their homomorphisms. First, some homomorphisms between FSVISs are introduced. After that, attribute reduction based on tolerance relation in a FSVIS is studied. Eventually, we get invariant characterizations of FSVISs based on some special homomorphisms under data compression.