The industry has expressed significant concern regarding the issue of parallel machines and the influence of learning and deterioration. This research investigates non-identical parallel machine scheduling, taking into account the simultaneous consideration of learning effects, deterioration, and past-sequence-dependent setup times. Due to the existence of uncertain parameters in real-world scenarios, the processing times and due dates are assumed to be triangular fuzzy numbers. A fuzzy nonlinear mathematical model with two objective functions is presented and solved using the fuzzy Chance Constraint Programming approach. The two objectives are the summation of earliness and tardiness, as well as makespan. To achieve an efficient near-optimal Pareto front for the problem, a hybrid NSGA-II and VNS multi-objective meta-heuristic is proposed and the results are discussed. Finally, the augmented ε-constraint method is utilized to address issues with small dimensions. The computational analysis demonstrates the effectiveness of this proposed algorithm in tackling problems, especially those with substantial dimensions.