Normal forms and truth tables for fuzzy logics

In this paper, we examine and compare De Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we show that there are normal forms and truth tables for classical fuzzy propositional logic and interval-valued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determining logical equivalence of two expressions in fuzzy propositional logic is a finite problem, and similarly for the interval-valued case. Turksen's work on interval-valued fuzzy sets is examined in light of these results.

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