Normal forms and truth tables for fuzzy logics
Classical representability of logical equivalence by means of (finite) truth tables is discussed. While the Boolean logics (algebras) require 2 truth values only, for the fuzzy logics (algebras) it is shown that 3 truth values are sufficient. Moreover, in the case of interval-valued fuzzy logics (algebras) it is enough to examine the logical equivalence by means of truth tables with 4 truth values. Normal forms in several special algebras (De Morgan, Kleene), fuzzy logics and interval-valued fuzzy logics are presented. The paper extends previous results on universal normal forms and truth tables of \textit{I. B. Türksen} [e.g., IEEE Trans. Fuzzy Syst. 6, 295-303 (1998)] and of the authors [Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 5, 223-238 (1997)].
scientific article; zbMATH DE number 1975909