Are fuzzy sets a reasonable tool for modeling vague phenomena?

In the paper, the indeterminacy phenomenon is discussed, that is, a phenomenon having two facets: uncertainty and vagueness. We argue that fuzzy sets are a reasonable mathematical tool for modeling of the latter. The necessary sound foundations of their theory can now be more easily established because of significant progress reached in the formal theory of fuzzy logic. Further direction in the development of fuzzy set theory is also discussed.