n-ary Fuzzy Logic and Neutrosophic Logic Operators

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built. Introduction. For the beginning let’s consider the Venn Diagram of two variables x and y , for each possible operator, as in Knuth’s table, but we adjust this table to the Fuzzy Logic (FL). Let’s denote the fuzzy logic values of these variables as 1 1 ( ) ( , ) FL x t f = where 1 t = truth value of variable x , 1 f = falsehood value of variable y , with 1 1 1 1 0 , 1 and 1 t f t f ≤ ≤ + = ; and similarly for y : 2 2 ( ) ( , ) FL y t f = with the same 2 2 2 2 0 , 1 and 1 t f t f ≤ ≤ + = . We can define all 16 Fuzzy Logical Operators with respect to two FL operators: FL conjunction ( ) FLC and FL negation ( ) FLN . Since in FL the falsehood value is equal to 1truth value , we can deal with only one component: the truth value. The Venn Diagram for two sets X and Y