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Many researchers and analysts are interested in evaluating the performance of a system with a network structure as a decision-making unit. In this regard, fuzzy network data envelopment analysis (FNDEA) is a noticeable and worthy method for evaluating the efficiency of a system with fuzzy data. Based on the structure of a fuzzy network system, which consists of at least two serial stages, an intermediate factor has an output nature for the first stage and an input nature for the second stage. Hence, it is inappropriate to allocate the same weight for each stage using this factor. Unfortunately, contrary to real-world conditions, all previous conventional FNDEA studies have considered the same role for intermediate factors to linearize or simplify models. For the first time, this study attempts to determine the upper and lower bounds of the overall efficiencies of a fuzzy two-stage series system and its subprocesses with unequal intermediate product weights.

The proposed model remains in its original nature as a complex combinatorial problem in the nonlinear programming category of NP-hard problems. A genetic algorithm (GA) is utilized as a metaheuristic algorithm, and a novel hybrid GA-FNDEA algorithm is presented to solve the problem.

The findings of the study outlined several theoretical contributions and practical implications, including as compensatory property of DEA, determining upper and lower bounds, improving efficiency in nonlinear systems, reducing computational burden, enhancing evolutionary algorithms and retaining real-world conditions.

Contrary to real-world conditions, all previous conventional FNDEA studies have considered the same role for intermediate factors to linearize or simplify models. For the first time, this study attempts to determine the upper and lower bounds of the overall efficiencies of a fuzzy two-stage series system and its subprocesses with unequal intermediate product weights.