Fish cages are crucial for the establishment of sustainable fish farms. The selection of fish cages is an essential subject to be examined for ensuring sustainability. This research introduces an advanced decision support model for the selection of fish cage types used in fish farming in reservoirs (R-FFs). The decision support model is based on multi-criteria decision-making (MCDM) approach and utilizes type-2 neutrosophic numbers (T2NNs). The importance levels of criteria are determined using the T2NN-Entropy method, and the ranking of fish cage types is achieved through the alternative ranking order method accounting for two-step normalization (AROMAN). The developed model is referred to as the T2NN-Entropy-AROMAN hybrid method and relies on expert opinions. Two advanced aggregation operators based on Yager t-norm and t-conorm operations, named T2NN Yager weighted arithmetic mean and T2NN Yager weighted geometric mean, are developed for aggregating T2NNs. The validity of these two aggregation operators is demonstrated. A real-life case study is developed to confirm the applicability of the T2NN-Entropy-AROMAN hybrid method. This case study focuses on the selection of fish cage types for the Artvin-Borçka R–FF in Artvin province, Turkey. The research results indicate that floating cages are the best alternative type for sustainable fish farming. Sensitivity analysis scenarios confirm the robustness of the research model and findings. The research findings, coupled with the developed model, offer valuable insights and guidance to decision-makers, researchers, and practitioners within the sector.