Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras

The aim of this article is to develop a representation theory of interval-valued Łukasiewicz–Moisil algebras; the concept of interval fuzzy sets involves the role that the notion of field of sets plays for the representation of Boolean algebras. This theory provides both a semantic interpretation of a Łukasiewicz interval-valued logic and a logical basis for the interval fuzzy sets theory.