ABSTRACT
Artificial intelligence.—One of the difficulties ordinary logic has in representing knowledge comes from the fact that calculating a truth value necessarily ends with either a true or a false, even though many situations call for verdicts in shades of gray (→LOGIC, REPRESENTATION, TRUTH). We know how to assign a gradual measure to propositions: their probability. However, while probability is considered suitable for representing uncertainty, other techniques are deemed necessary for imprecise knowledge, if for no other reason than because calculating probabilities is too complicated to be compatible with the cognitive processing of this kind of knowledge. Authors have been proposing other techniques for quite some time (for example, Jan Lukasiewicz in 1920). In 1965, Lotfi Zadeh introduced the term fuzzy subset to refer to the idea of a grade µ E(e) of membership of element e in set E. Given that the interpretation of a unary relation is a subset, this idea can be extended by stating that the degree of truth of atomic proposition P(A) is equal to µ p(a), where a is the element that interprets constant A, and p is the subset that interprets relation P. A fuzzy logic is thereby generated.
