Fuzzy and Boolean Logics are equally expressive and one is nothing more than syntactic sugar for the other. I'm honestly trying to get convinced otherwise.
Here's my argument:
In Boolean logic, $x \in X$ is a predicate which evaluates to one of two values, and we take one of those values to signify truth. Let us denote $V_B = \{0, 1\}$ to be the logical values of Boolean Logic.
In Fuzzy logic and non-conventional logics like Tri-State logic, $x \in X$ is a predicate which evaluates to $v$ where $v \in V$ and $V$ is the set of logical values pertaining to the logic in question.
Now here's what I mean when I say that Fuzzy Logic is at most as expressive as Boolean Logic:
Let $F$ parse a valid statement $s$, the answer being $v$: $$F(s) \to v$$
Now let $B$ parse $v = k$, which is a valid statement in Boolean Logic: $$B(v=k) \equiv B(F(s)=k)$$ $$B(v=k)\in \{0, 1\}$$
So we've changed the question:
What is the degree of set membership of x in X?
To:
Is this k the degree of set membership of x in X?
We can boil down any statement in Fuzzy Logic (or any other for that matter) to a statement in Boolean Logic.
Conclusion: Fuzzy Logic is fundamentally offering nothing more to the table than Boolean Logic already does.