Suppose that I have a proposition, represented by variable $p$. It is my understanding that in fuzzy logic, $p$ may have a truth value $x$ where $\{x \in \mathbb{R} \mid 0 \leq x \leq 1\}$.
Now suppose that if $x = 0$, then it would imply that $p$ is "completely false". Similarly, if $x = 1$, then it would imply that $p$ is "completely true". I would also like to establish that if $x$ was between $[0, 0.5)$, then $p$ would be on a varying degree of "somewhat false" truth value. Similarly, if $x$ was between $(0.5, 1]$, then $p$ would be on a varying degree of "somewhat true" truth value.
Now... how would I be able to deal with $x = 0.5$? What kind of truth value would it have? Can such truth value even exist in practice (e.g. artificial intelligence)?
I would appreciate any informative input! Thank you!
Although it should have been obvious, I have not considered carefully enough that fuzzy logic is considered an infinite-valued logic and not a two-valued logic. Therefore, the principle of bivalence, which is applied to two-valued logic, does not apply to infinite-valued logic. Hence, $x = 0.5$ should be carefully considered as a "partially true and partially false" (i.e. $50\%$ true and $50\%$ false) value. This is useful for characterizing things like quantum indeterminacy, etc.