model fuzzy assignment problem

Question

i wanna ask something about fuzzy assignment, why in fuzzy assignment problem specially in min z form didn't using $tilde{x}$ in $x_{ij}$ meanwhile it is used in $c_{ij}$ and also $z$.

\begin{align*} \min \widetilde{z}=&{\sum^{n}_{i=1}}{\sum^{n}_{j=1}}\widetilde{c}_{ij}x_{ij} \end{align*}

Answer 1

The $x$ has no tilde because $x$ is not fuzzy. Instead, $x$ is a binary decision variable whose value is to be chosen to minimize the objective function subject to the constraints.