Disasters can cause many casualties and considerable destruction mainly because of ineffective preventive measures, incomplete preparedness, and weak relief logistics systems. After catastrophic events happen, quick and effective response is of great importance, so as to having an efficient logistic plan for distributing needed relief commodities efficiently and fairly among affected people. In this paper, we propose a fuzzy multi-objective, multi-modal, multi-commodity logistic model in emergency response to disaster occurrence, to assign limited resources equitably to the infected regions in a way to minimize transfer costs of commodities as well as distribution centers activation costs, and maximizing satisfied demand. In the proposed model, we have determined the optimal place of distribution centers among candidate points to receive people donations as well as sending and receiving different kinds of relief commodities. The amount of voluntary donations is not known precisely and is estimated with uncertainty, so we have used fuzzy parameters for them. The number of victims immediately after disaster is vague and is estimated indecisively though we have considered it as a fuzzy demand. A case study has been displayed to test the properties of the optimization problem that shows efficiency of this formulation in experiment.