On Models in Fuzzy Propositional Logic

摘要

A model theory of fuzzy propositional logic is considered. The basic frame for fuzzy propositional logics are Zadeh-algebras, I.e., special quasi-Boolean algebras, where valuation functions are universes of these algebras. There are two levels of truth-values, numerical (usually the unit interval[0,1], or in general, a lattice L) and linguistic. Linguistic truth-values are fuzzy subsets of the set of numerical truth-values. Fuzzy model is defined based on numerical truth-values, I.e. it is the set of designated truth-values. Its linguistic label is true. Truth conditions and the concepts validity, satisfiability, refutability, and invalidity are considered.