Abstract

Starting from the Russel’s studies on the limits of the empiricism, some considerations about the concept of vagueness, are recalled in order to stress the motivations and the development of a foundational context for the fuzzy sets. The description of the facts of the physical reality expressed in terms of fuzzy sets draws its origin from the objective of “calculating with words” being vagueness in the facts and in the language representing them. The unique operations that satisfy a system of reasonable requirements are defined. A measure of the degree of fuzziness, the fuzzy entropy, is defined in terms of a functional over the fuzzy sets.