Abstract
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 /spl ap/ 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.
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