Abstarct: Location problems are one of the most important operation researches which are used in the field of location of subway stations , buss stops , fire stations and etc. p-median problems are very significant in the field of location so that in which many math scientists have been interested. In p-median problem, the sets of edges and vertex demands are assumed in a crisp form but in reality the sets of edges and vertex demands or a mixture of both are not crisp. In other words, in reality almost always fuzzy data and numbers are available. In this these we work on the issue how to prepose the models of p-median problem and how to solve them appropriately. We also intend to understand how much cost the solutions baxsed on eliminating one less significant and unnecessary vertex can reduce. Or in order to decrease the optimal cost as much as needed how much vertex demandss should be declined to make demanders needs satisfied.