Data envelopment analysis (DEA) is a non-parametric approach that measures the efficiency of a decision-making unit (DMU) statically and requires crisp input-output data. However, as a performance analysis tool, DEA overlooks the inter-relationship present among periods, and in many real applications, it is challenging to define the information for variables like customer satisfaction, service quality, etc. in precise form. To fix this, the present paper develops a novel parabolic fuzzy dynamic DEA (PFDDEA) approach that not only measures the system and period fuzzy efficiencies of DMUs by considering the inter-dependence among periods in the presence of undesirable resources but also handles data as parabolic fuzzy numbers (PFNs). It evaluates fuzzy efficiencies in a dynamic environment by distinguishing the role of links as inputs/outputs. In the proposed approach, system fuzzy efficiencies are estimated by solving the proposed PFDDEA models based on the α-cut approach that guarantees the shape of the membership function of the system fuzzy efficiencies obtained at different α-levels as PFNs. Further, an algorithmic approach for measuring period fuzzy efficiencies based on the concept of α-cuts and Pareto’s efficiency is developed that leads to the estimation of the shapes of their membership functions. Finally, a relationship has been derived between upper (lower) bound system efficiency and upper (lower) bound period efficiencies at each α-level. To the best of our knowledge, this is the first attempt that dynamically evaluates fuzzy efficiencies (system and period) of DMUs when the data for the inputs/outputs/links are PFNs. To validate the applicability and robustness of the proposed approach, it is applied to eleven Indian banks for two periods 2019–2020 and 2020–2021, including loss due to non-performing assets (NPAs) as an undesirable output and unused assets as a link between periods. Here, NPAs are the bad loans that cease to generate income for the banks. The findings of the study (i) depict the system and period efficiencies as PFNs, (ii) conclude that the Federal Bank (FB) is the most efficient and Punjab National Bank (PNB) is the least efficient bank in the system and all periods, and (iii) provide implications that are highly valuable for bank experts to consider the impact of NPAs and unused assets for improving underperformed banks. These findings indicate that the proposed PFDDEA approach is highly useful for ranking/benchmarking in a dynamic manner keeping in view the presence of uncertain data variables represented as PFNs.