Expert Systems with Applications, v. 164. Abstract: Traditional Data Envelopment Analysis (DEA) models usually consider decision-making units (DMU) as black boxes that consume a set of inputs to produce a set of outputs and ignore the units’ internal structure. In literature, two-stage DEA models have been introduced and developed to deal with the inner workings of such DMUs; however, models in the extant literature can only be used to assess technologies with precise inputs and outputs. In this study we present an innovative two-stage DEA model for DMU evaluation in the presence of imprecise data, which are modeled using triangular fuzzy values in this study. We also innovate by including the treatment of undesirable outputs. We propose some alternative two-stage DEA network models with undesirable outputs in a full-fuzzy mode that are either directional or radial and are embedded within a multi-objective linear planning structure based on fuzzy triangular numbers. We also propose a method to solve fuzzy programming models in the presence of undesirable pollutant outputs from production processes such as greenhouse gas emissions, harmful effluents, among others. Our proposed model is then applied to a real case of 15 ammonia-manufacturing units in the Iranian petrochemical sector. The promising results that we obtained in our research and their implications for theory and practice are then presented and discussed.