Have Fuzzy Sets Anything to Do with Vagueness?

From their inception, fuzzy sets were introduced by Zadeh [55] with a view to formalize human knowledge in engineering problems. This implies fuzzy sets had somehow to come to grip with some aspects of natural language modeling, and in particular, with the concept of vagueness, i.e., the idea that the extension of some natural language predicates lacks clear truth conditions. The claim that fuzzy sets are a basic tool for addressing vagueness of linguistic terms has been around for a long time. For instance, Novák [38] insists that fuzzy logic is tailored for vagueness and he opposes vagueness to uncertainty. Nevertheless, in the last thirty years, the literature dealing with vagueness has grown significantly, and much of it is far from agreeing on the central role played by fuzzy sets in this phenomenon. Following Keefe & Smith [42], vague concepts in natural language display three features: