  In the present work, we wanted to find the possible way in order to make the
equivalence between non-commutative and Finsler geometries as two useful
mathematical tools. Based on this purpose, we were concerned to search this
possibility by investigating the massive gravity black holes. Firstly the
Lagrangian of the system is introduced and then it is rewritten in the
non-commutative regime by definition of the new variables. On the other hand,
we focus on the Finsler geometry in order to find a Finslerian function which
is equivalent to the mentioned non-commutative Lagrangian under special
conditions. Also, the effective potential of the system was calculated as a
part of the corresponding conditions.
