Managing minority opinions in risk evaluation by a delegation mechanism-based large-scale group decision-making with overlapping communities

Energy performance contracting (EPC) mechanism is a good choice for conducting energy-saving renovation projects of public buildings. Furthermore, risk analysis is critical to smoothly implement these EPC projects. Therefore, this paper intends to set up a large-scale group decision-making (LGDM) framework based on delegation mechanism to rank risk factors of EPC projects. Firstly, some risk factors and evaluation criteria are identified. Meanwhile, the assessment is expressed as picture fuzzy numbers (PFNs) to handle conflicting opinions and refusals. Then, a novel bidirectional projection measure that considers both distance and included angle is defined, which can better describe the difference between two PFNs. Next, this paper uses a suitable algorithm to cluster experts and presents a delegation mechanism to allocate trust weights of external experts to internal experts. Then, a new method to protect minority opinions is presented. In addition, we use preference risk coefficient to integrate the uncertainty of decision information in consensus-reaching process (CRP), which reduces the risk of LGDM. We come up with an extended MULTIMOORA method to make full use of three parts of MULTIMOORA method. Moreover, the proposed framework is successfully implemented in a case study and some risk mitigation measures and management implications are presented.