In fuzzy logic statements are translated into elastic constraints and the meaning is computer directly via nonlinear techniques. The degree of truth is a measure of the coherence between a proposition about the world and the state of the world. Zadeh defines a procedure to compute the meaning, i.e. that constraint, through non-linear programming techniques. A proposition can be true, false, partially known or vague with a degree of vagueness. Zadeh's theory of fuzzy quantities assumes that things are not necessarily true or false, but things have degrees of truth.
Fuzzy logic is a multi-valued logic that extends classical logic.
In fuzzy logic each application of the inference rule erodes the truth of the resulting proposition. As for Duhem's principle of incompatibility, the certainty that a proposition is true decreases with any increase of its precision. A fuzzy set is a set of elements that belong to a set only to some extent. Each element is characterized by a degree of membership. Each set can be subset of another set with a degree of membership.