Reliability is the measure of the result of the quality of the system over a long run. The reliability-redundancy allocation problem (RRAP) aims to ensure high systems reliability in the presence of optimally redundant systems components. This is one of the most important design considerations for the systems designers. Several researchers have addressed this important issue during last few decades. However, due to the embedded uncertainty in the parameters of the system components, reliability as well as the costs of the whole system fits very well to be modeled as fuzzy quantity. We therefore modeled this problem as a fuzzy multi-objective optimization problem (MORRAP) that is addressed using the popular multi-objective evolutionary algorithm, NSGA-II (non-dominated sorting genetic algorithm-II). We have considered the based MORRAP with fuzzy type-2 uncertainty. As far as we know, no research has been reported where MORRAP was considered under type-2 fuzzy uncertainty. A typical numerical example is included and results are compared showing that our approach outperforms other recently reported results.