<p>This study deals with a redundancy allocation problem (RAP) for a series–parallel system with multiple choice technologies in each subsystem. In this system, the aim of the study is to solve a multi-objective optimization problem by maximizing the system reliability and minimizing the system cost simultaneously, subject to the volume and weight constraints. Here, three different models have been considered: (i) A crisp model, (ii) A fuzzy model with uncertain parameters, and (iii) A fuzzy model with both uncertain parameters and constraints. The fuzzy parameters have been defuzzified by using two methods: graded mean integration representation (GMIR) and signed distance method (SDM). All the multi-objective optimization problems have been solved by applying two methodologies, viz. elitist non-dominated sorting genetic algorithm (NSGA-II) and Global Criterion Method (GCM). To justify all these models, four numerical examples have been considered and solved. After solving the problems, it is revealed that the single compromise solution obtained by GCM lies on the Pareto optimal solutions of NSGA-II. This study also informs us about the impact of fuzzy constraints on the model. Furthermore, the results have been discussed using two defuzzification methods. Also, to observe the impact of some vital parameters on system reliability and system cost, sensitivity analyses have been carried out. From this analysis, it is possible to determine how to set the parametric values and how the component attributes influence the results.</p>