A novel method for solving neutrosophic data envelopment analysis models based on single-valued trapezoidal neutrosophic numbers

Neutrosophic data envelopment analysis (Neu-DEA) is a mathematical tool for calculating the performance of decision-making units (DMUs) in a neutrosophic environment. In this paper, a novel ranking function is developed specifically for single-valued trapezoidal neutrosophic numbers (SVTrNNs). The properties of this new ranking function have also been extensively studied. We develop the Charnes–Cooper–Rhodes models in the context of SVTrNNs to measure the efficiency of homogeneous DMUs. Additionally, we propose a unique solution process by incorporating the newly developed ranking function, which allows for the conversion of the neutrosophic DEA model into a corresponding Crisp LP model. This approach offers an efficient and effective tool of measuring the DMU efficiency in a neutrosophic environment. The reference set or peer group is defined for inefficient DMUs, which enables them to improve their efficiency score by following their peers. Two different approaches are suggested as potential ways to completely rank the DMUs, i.e., the reference set- and the super-efficiency-score-based ranking approaches. The validity and existence of the proposed models are demonstrated by providing an illustrative example, and the results are compared to an existing approach. The proposed Neu-DEA model is employed to assess the efficiency of the 12 major seaports in India, and it yields superior outcomes compared to the currently existing models.