The location allocation problem is one of the most attractive optimization problems that is widely used in the real world. Therefore, any attempt to bring this problem closer to real-world conditions would be significant and useful. In this paper, we utilize fuzzy logic due to the uncertainty of parameters in the real world. That is the weights (the amounts of demands of customers) and variables (the coordinates of the optimal place) are both considered fuzzy numbers. If these variables are considered definitively, due to various conditions and reasons, it may not be possible to acquire land or build a facility center in it, so we also considered this variable in a fuzzy way and a facility center area was obtained, that certainly, the decision maker can find the right place more easily. To solve the fuzzy problem a new approach based on presenting the problem in the form of equivalent expressions is proposed. This equivalent problem is solved using fuzzy arithmetic. Manuscript profile