The present paper aims to propose a fuzzy multi-objective model to allocate order to supplier in uncertainty conditions and for multi-period, multi-source, and multi-product problems at two levels with wastages considerations.  The cost including the purchase, transportation, and ordering costs, timely delivering or deference shipment quality or wastages which are amongst major quality aspects, partial coverage of suppliers in respect of distance and finally, suppliers weights which make the products orders more realistic are considered as the measures to evaluate the suppliers in the proposed model. Supplier's weights in the fifth objective function are obtained using fuzzy TOPSIS technique. Coverage and wastes parameters in this model are considered as random triangular fuzzy number. Multi-objective imperial competitive optimization (MOICA) algorithm has been used to solve the model,. To demonstrate applicability of MOICA, we applied non-dominated sorting genetic algorithm (NSGA-II). Taguchi technique is executed to tune the parameters of both algorithms and results are analyzed using quantitative criteria and performing parametric.