A multi-criteria decision-making framework for risk ranking of energy performance contracting project under picture fuzzy environment

Identifying the priority of risks as regards energy performance contracting (EPC) projects is one of the main issues faced by energy service companies. Considering the complexity and uncertainty of EPC mechanism, this study attempts to formulate a hybrid fuzzy multi-criteria decision-making framework with picture fuzzy information to rank the risk factors of EPC projects. The proposed framework not only considers the interrelationship among criteria but also considers the decision-maker's bounded rationality and behavioural psychology. First, to effectively express the uncertainty and fuzziness of risk and environment, risk evaluation is expressed as picture fuzzy numbers. Subsequently, the new distances of picture fuzzy sets are proposed to fully use picture fuzzy information. Meanwhile, considering the interrelationship among criteria, an optimisation model based on the maximizing deviation method and Bonferroni mean distance of picture fuzzy sets is established to determine the weight vector of criteria with incomplete weight information. Furthermore, a prospect theory-based multi-attributive border approximation area comparison (MABAC) method is proposed to rank the risks and identify the priority of risks by reflecting the decision-maker's bounded rationality and behaviour psychology. In addition, the proposed framework is successfully implemented in a case study of a hotel's energy efficiency retrofit. Results show that the proposed framework is an effective and practical decision tool for risk ranking problems under picture fuzzy environment. Finally, the detailed risk mitigation, energy-saving performance and implications are presented to provide a reference and suggestion for other projects.