Efficiency Analysis and Ranking of the Decision-Making Units Using Bipolar Fuzzy Data Envelopment Analysis

Abstract

This manuscript introduces a novel extension of Fuzzy Data Envelopment Analysis (FDEA) by incorporating Triangular Bipolar Fuzzy Numbers (BTFNs), thereby proposing the Bipolar Fuzzy DEA (BFDEA) framework to better model environments with uncertainty and conflicting information. The authors define a magnitude function to transform the proposed BFDEA model into a crisp linear programming model, enabling the computation of efficiency scores for Decision-Making Units (DMUs). To address the challenge of ranking fully efficient units, a bipolar super-efficiency model is developed, complemented by a benchmarking methodology that identifies peer DMUs to guide performance improvement of each inefficient DMU. The approach is clearly illustrated through a numerical example involving ten DMUs, with detailed evaluation, ranking, and benchmarking results and compared with the existing fuzzy model. The paper contributes significantly to the literature by enhancing DEA's ability to handle both positive and negative aspects of fuzziness, thus offering a more expressive and realistic efficiency analysis framework in complex decision-making environments.

Received: 10 July 2025 | Revised: 22 September 2025 | Accepted: 9 October 2025

Conflicts of Interest

The author declares that he has no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Kshitish Kumar Mohanta: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing — original draft, Writing — review & editing, Visualization, Supervision, Project administration.