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A metaheuristic search procedure modified by fuzzy logic and fuzzy set theory for solving p-facility location problems is proposed in this paper. Known as p-median problem, as well, the objective is to find p centers (locations) in a network in order to minimize (maximize) the average distance between demand nodes and their medians. The proposed approach employs Greedy Randomized Adaptive Search Procedure (GRASP) modified by grading the distances from locations weighted by membership functions or fuzzy rules. In so doing, a novel approach named Fuzzy Greedy Randomized Adaptive Search Procedure (FUGRASP) is presented. In order to verify the feasibility of the proposed method, p centers are computed to minimize the average distances among cities according to their respective air-traffic importance.