In the face of diverse and conflicting factors affecting emergency water supply (EWS) decisions, ensuring sufficient drinking water provision for communities emerges as a critical and intricate challenge. Compounding this complexity is the presence of vague and imprecise data, complicating the evaluation and selection process. To tackle these challenges, this study introduces an extended fuzzy multi-criteria group decision-making (FMCGDM) model, leveraging compromise solutions and relative preference relations, specifically tailored for EWS situations. The proposed model employs linguistic variables with multiple experts’ judgements to rate the alternatives versus conflicting criteria and assign weight to these criteria. By utilizing triangular fuzzy numbers, the model effectively handles information imprecision, enabling nuanced evaluations and distinguishing among potential alternatives. Employing a relative preference relation, the model computes distance values between alternatives and ideal or anti-ideal solutions, aiding in decision-making. Finally, the practical application and computational effectiveness of the model are demonstrated through a real-life case study on EWS in Iran. The results show that the mobile water treatment units and packaged water alternatives received the highest score, placing first and second in the order ranking, respectively, while the existing distribution systems were deemed most inappropriate for the EWS situation in the case study.