Novel fuzzy game two-stage DEA model: application in sustainable road transport system

Abstract

This study aims to develop an integrated decision-support framework for evaluating the sustainability performance of road transport systems by explicitly addressing inter-stage conflicts, shared inputs and data uncertainty. Specifically, it seeks to measure and coordinate energy and economic value-added efficiency within a two-stage structure using game theory and data envelopment analysis, thereby supporting more informed and balanced managerial decision-making. The study proposes a novel two-stage DEA model with shared inputs, where the first stage evaluates energy efficiency and the second assesses economic value-added efficiency. Game theory is embedded to model both non-cooperative (leader–follower) and cooperative interactions, deriving maximum and minimum efficiency bounds. To accommodate imprecise data, fuzzy extensions are developed using triangular fuzzy numbers and the a-cut approach, with nonlinear models linearized for computational tractability. The methodology is empirically applied across 30 provinces in Iran. The study shows that non-cooperative strategies yield uneven efficiency outcomes, benefiting dominant stages at the expense of overall system performance. Conversely, the cooperative game-theoretic DEA model enhances total system efficiency while ensuring minimum acceptable efficiency levels for energy and economic value-added stages. Additionally, the efficiency rankings are sensitive to uncertainty, highlighting the need for fuzzy modeling in transport sustainability assessments. Robustness analyses validate the stability of efficiency scores and rankings amid data changes, increasing the results’ reliability for managerial applications. This study is among the first to integrate game theory, two-stage DEA with shared inputs and fuzzy modeling into a unified framework for sustainability assessment of road transport systems. Unlike prior studies that ignore inter-stage conflicts, the proposed approach explicitly models strategic interactions between stages and provides coordinated, bargaining-based efficiency solutions. The framework offers decision-makers a practical and robust tool for performance evaluation and resource allocation under uncertainty, with direct applicability to complex multi-stage systems beyond the transport sector.