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Occurrence of natural disaster inflicts irreparable injuries and symptoms on humans. In such conditions, affected people are waiting for medical services and relief commodities. Thus, quick reaction of medical services and relief commodities supply play important roles in improving natural disaster management. In this paper, a multi-objective non-linear credibility-based fuzzy mathematical programming model under uncertainty conditions is presented, which considers two vital needs in disaster time including medical services and relief commodities through location of hospitals, transfer points, and location routing of relief depots. The proposed model approaches reality by considering time, cost, failures probability in routes, and parameters uncertainty. The problem is first linearized and then global criterion method is applied for solving the multi objective model. Moreover, to illustrate model efficiency, a case study is performed on region 1 of Tehran city for earthquake disaster. Results demonstrate that if Decision-makers want to meet uncertainty with lowered risk, they have to choose a high minimum constraint feasibility degree even though the objective function will be worse.