Consensus-based group decision-making methods with probabilistic dual hesitant fuzzy preference relations and their applications

Probabilistic dual hesitant fuzzy sets (PDHFSs) have good flexibility and integrity in expressing fuzzy and uncertain information. However, some crucial problems related to PDHFSs remain unsolved, such as how to define probabilistic dual hesitant fuzzy preference relations (PDHFPRs) and solve group decision-making (GDM) problems with PDHFPRs. This paper establishes the concept of PDHFPRs and investigates consensus-based GDM methods with PDHFPRs. First, a new distance measure is proposed to quantify the difference between two PDHFPRs, which does not increase the virtual elements of membership and non-membership degrees, and can contain all distance combination of membership and non-membership elements. Therefore, the distance calculation results are not affected by the subjectivity of decision-makers (DMs). Second, the consensus measures for PDHFPRs are proposed, which are effective tool to measure the consensus level among DMs. Moreover, two consensus-based GDM methods are proposed, which can improve the group consensus level for PDHFPRs by changing the PDHFPR with the worst consensus level or modifying the weights of DMs. Finally, the proposed methods are applied to the location selection of large-scale industrial solid waste treatment facilities. The comparison with existing methods illustrates the validity and feasibility of the proposed methods.