A Novel Pythagorean Fuzzy Data Envelopment Analysis Model: An Assessment of Indian Public Sector Banks

Fuzzy data envelopment analysis (FDEA) is an efficient modeling technique to rank decision-making units (DMUs) with imprecise inputs/outputs. It is a linear programming problem that constructs an optimal frontier line, known as an efficient frontier. The role of the efficient frontier is to distinguish between the efficient DMUs with inefficient DMUs such that all efficient DMUs lie on the frontier line. Whereas the inefficient DMUs are enveloped by the frontier line. This optimization problem aims to improve the efficiency score of each inefficient DMU, that is, to move them to the efficient frontier. In this study, we propose a novel approach called the Pythagorean approach, which is both input and output oriented. The proposed approach is implemented in the CCR model, and a new version of the BCC model is introduced, namely a novel Pythagorean BCC model. The deterministic form of the Pythagorean BCC model is extended to a fuzzy environment to deal with the vagueness of the given dataset. In the paper, a new form of a non-linear fuzzy number, namely a sine-shaped fuzzy number, has been introduced to display the higher order of uncertainty. Consequently, the Pythagorean BCC model is further extended to a novel Pythagorean fuzzy BCC model. The model's efficacy is finally tested in the Indian public sector banks.