Impact of fuzzy normal forms on knowledge representation

Fuzzy normal forms can be generated with an application of “Normal Form Generation Algorithm” on fuzzy truth tables. This takes place at the third level of knowledge representation, i.e., propositional level. It is shown that at least three distinct sets of normal forms can be generated depending on the axioms one is willing to impose on the propositional fuzzy set and logic theories. All are conjunctive-disjunctive and complement based De Morgan logics with the following three classes of axioms that identify each general class of fuzzy normal forms in order of least to most restrictive set of axioms in the following sense: 1) boundary and monotonicity; 2) boundary, monotonicity, associativity and commutativity; and 3) boundary, monotonicity, associativity, commutativity and idempotency