The main goal of this paper is to solve a fuzzy multi-objective reliability redundancy allocation problem (MORRAP) for xj -out-of- mj series-parallel system. We consider that system reliability and system cost are two conflicting objectives. Due to the incompleteness and uncertainty of input information, we formulate the objectives by considering the reliability and cost of each component as a triangular fuzzy number (TFN). Here, the fuzzy multi-objective optimization problem of system reliability and cost is analyzed simultaneously using our proposed fuzzy rank-based multi-objective particle swarm optimization (FRMOPSO) algorithm. Comparing the results of FRMOPSO with standard particle swarm optimization (PSO), we see that better optimum reliability and cost have been achieved in the FRMOPSO technique. To illustrate the effectiveness of our proposed technique, we consider the problem of the over-speed protection system of gas turbines containing two mutually conflicting reliability and cost objectives with entropy and several other constraints. We present graphically the effect of optimum system reliability and cost with respect to the percentage change of different parameters. We also compare the convergence rate of FRMOPSO with PSO. Our proposed algorithm shows better results.