I am studying fuzzy logic and the implication operator. Suppose we are given the implication "IF $x$ is $A$ THEN $y$ is B" with $A,B$ fuzzy sets so $A(x), B(x) \in [0,1]$ are the membership functions. The definition for implication then is $$IMP(x,y) = min(1, 1 - A(x) + B(y)).$$
The definition makes sense for $A(x) = 0$ as the implication then yields $IMP(1,y) = 1$ (since $false \implies x$ is always true).
But why not define the implication similar to the standard logic implication?
As $A \implies B$ is equal to $\neg A \vee B$, we could define $$IMP_{alternative}(x,y) = \neg A(x) \vee B(x)= A^c(x) \vee B(x) = max \{ 1 - A(x), B(x)\}.$$ The above definition makes in my opinion more sense...