Put the name of the matrix tikz besides the figure besides on the left at the middle

Question

I have done a matrix with Tikz. It is missing just a last point : set on the left in the middle the name of the matrix such I could have : F_matrix = [figure_tikz]

I tried :

$F_{\text{Big Fisher}}=$
\begin{figure}
  \includestandalone[width=\textwidth]{tkiz_big_fisher}%     without .tex extension
  % or use \input{mytikz}
  \caption{Methodology}
  \label{fig:bigfisher}
\end{figure}

but not succeeded.

Could you tell me please how to add this text at this position (middle on the left with the symbol '=' ?

UPDATE : I didn't manage to include the Tikz figure in my main Latex source.

I am obliged to generate first a PDF for my Tikz figure and after include it by doing :

 \begin{figure}
  $F_{ij}=$\includegraphics{tikz_big_fisher.pdf}
  \caption{Methodology}
  \label{fig:bigfisher}
\end{figure}

But the term $F_{ij}$ is at the bottom left of matrix, like this :

How to circumvent this issue ? I would like this text to be at the middle on the left like a classical "Matrix_name" = tikz figure.