Filtration-and-weighting-based consistency of distributed preference relations for multi-criteria group decision-making

Consistency of distributed preference relations (DPRs) is an essential prerequisite for modeling and solving decision-making problems with DPRs. Existing consistency of DPRs is developed based on current preference information of decision-makers, which increases the burden of providing alternative assessments. In addition, more current preference information may not be available for practical decision-making problems. To address this issue, this paper studies the consistency of DPRs based on the historical preference information of decision-makers, which is filtered and weighted to guarantee its quality, and develops the filtration-and-weighting-based consistency (FWBC) of DPRs. An abnormal DPR filtration process is first designed based on the modified Z-score to improve the effectiveness of historical DPRs, and a normal DPR weighting process is then constructed based on the newly defined difference measure between DPRs to highlight their contribution degrees in characterizing historical preferences of decision-makers. After the filtration and weighting preprocessing, the historical DPRs are used to create a consistency interval to verify the consistency of DPRs. To demonstrate the validity and applicability of the FWBC of DPRs, it is used to model a multi-criteria group decision-making method, which is applied to a new ultrasonic imaging technology import problem for a tertiary hospital in Hefei, Anhui, China.