Fuzzy Logic Based on Zadeh Operators

Zadeh operators for conjunction, disjunction, and negation are not considered a good semantic basis for any mathematical logic. In this paper, fuzzy models are specified by Zadeh operators along with a recursive definition of the truth values of implication formulas (as opposed to standard implication truth functions). These models are characterized by a subset of classical first-order logic. This subset is specified as a sequent calculus whose negation rule is different from classical negation inference rules. The recursive implication truth function and the logical characterization justify the use of Zadeh operators in fuzzy systems.