This study addresses the critical challenge faced by organizations in selecting an optimal subgroup of decision-making units (DMUs). Such a selection procedure can significantly influence efficiency, profitability, and strategic development. Recognizing the limitations of existing methods in handling inexact data and incorporating managerial preferences, this study proposes a novel framework that integrates data envelopment analysis (DEA) with binary linear programming models. The model applies belief-degree–based representations of uncertainty to capture imprecise inputs and outputs. For this model, two solution approaches—namely, chance-constrained programming and expected value approaches—were developed. These approaches are suitable for real-world applications using standard optimization software. The effectiveness of the proposed method was validated through a case study in Iran’s petrochemical industry, where it successfully identified the optimal technology for a new refinery unit while balancing efficiency and profitability under uncertainty. This work is the first study in the literature to combine DEA and binary linear programming under belief-degree–based uncertainty for DMU selection, offering a systematic, practical, and computationally efficient solution, with recommendations for future research to explore alternative uncertainty modeling techniques and broader industrial applications.