This study deals with a redundancy allocation problem (RAP) for a series-parallel system with multiple choice technologies contained in each subsystem. The aim of this study is to solve the multi-objective optimization problems by maximizing the system reliability and minimizing the system cost subject to the volume and weight constraints considering three different cases such as (i) crisp, (ii) fuzzy and (iii) fuzzy with ambiguity and vagueness. These 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. Then the simulated results have been discussed with respect to different cases and methodologies. Also to observe the impact of some vital parameters on system reliability and system cost, sensitivity analyses have been carried out.