On the concept of qualitative fuzzy set

Following T.Y. LIN vague concepts such as “high” or “small” (“amount of money” as linguistic variable) should be described by classes of “equivalent” fuzzy sets on a fixed suitable universe U. Furthermore LIN proposed to generate such classes by factorization of the fuzzy power set FP(U) of U with respect to a given equivalence relation ≈ on FP(U). By three examples we show that this approach is not successful if we intend to shift algebraic operations with fuzzy sets to classes generated by equivalence relations. Using a KRIPKE-style semantics approach we can introduce a sensible concept of a qualitative fuzzy set and, furthermore, sensible algebraic operations with such sets. The concept of multi-fuzzy set introduced by LIN is a special case of our concept of context-depending fuzzy set