In propositional Gödel logic, one can imagine a new operator $=$ as
$V(\phi = \psi) = \begin{cases}1,&\text{iff }V(\phi) =V(\psi)\\0,&\text{otherwise}\end{cases}$
with $V$ being the corresponding interpretation.
My question is if someone could imagine a formulas made up from the classic connectives($\land$,$\to$, $\lor$,$\neg$) which would be equivalent for this.
My first consideration was simply the connective $\leftrightarrow$ which fulfills this property in classical logic. But in case of Gödel(fuzzy) logic, it doesn't hold for the definition for 0.
Over Gödel logic, your operator is interdefinable with Baaz’s delta: $\phi=\psi$ can be defined as $\Delta(\phi\leftrightarrow\psi)$, and conversely, $\Delta\phi$ can be expressed as $\phi=\top$. It is not definable in Gödel logic alone.