A multi-criteria group decision-making method with fuzzy preference relations based on filtration-and-weighting-based triangular bounded consistency

In multi-criteria group decision-making (MCGDM) problems with incomplete fuzzy preference relations (FPRs), the consistency based on bounded rationality is preferred to depend on the historical preferences of decision makers to generate complete FPR matrices. There are two factors in influencing the effect of historical preferences on complete FPR matrices and further decision makers' satisfaction of group solutions. One is the effectiveness of historical preferences and the other is their relative weights. On this basis, this paper proposes a new MCGDM method with FPRs based on the filtration-and-weighting-based triangular bounded consistency (FWBTBC), where historical FPRs between three adjacent pairs of alternatives are characterized by triangles and these two factors are considered comprehensively. A triangle filtration process is designed based on the Grubbs criterion to filter the abnormal triangles in the collected ones. A weight determination process is developed, where a distance measure between remaining triangles is constructed to calculate their weights. Based on the combination of the two processes, the FWBTBC of FPRs is created and then the proposed method is presented. The validity of the proposed method is demonstrated by its application in analyzing a drainage tube supplier selection problem for a tertiary hospital located in Hefei, Anhui, China.