Necessary and sufficient conditions for fuzzy truth values to form a de Morgan algebra
Different fuzzy logics were shown to be particular cases of many kinds of algebras, such as Lukasiewicz algebra, Heyting algebra, de Morgan algebra, Kleene algebra, etc. In this paper, following the original definitions of fuzzy set operations proposed by L. A. Zadeh, we consider the set of all possible fuzzy truth values, the set which contains linguistic truth values such as "true", "very true", "more or less true", etc. We show that if we impose some conditions on fuzzy truth values, then the resulting set of fuzzy truth values with naturally defined logical operations forms a, de Morgen algebra.
fuzzy truth value de morgan algebra fuzzy logic