Consistency analysis and priority weights of multiplicative trapezoidal fuzzy preference relations based on multiplicative consistency and logarithmic least square model
Affiliations: [a] School of Mathematical Sciences, Anhui University, Hefei, Anhui, China
| [b] Department of Civil Engineering, Anhui Communications Vocational and Technical College, Hefei, Anhui, China
| [c] China Institute of Manufacturing Development, Nanjing University of Information Science and Technology, Nanjing, China
Abstract: Consistency and the priority vector are two important issues in preference relations. As one of preference relations, multiplicative trapezoidal fuzzy preference relation (MTFPR) is an effective form of vague and imprecise information when decision maker (DM) express his/her opinions by comparing alternatives or criteria with each other in group decision making (GDM). Therefore, it is meaningful to discuss the consistency and the method for deriving priority vector of MTFPRs. In this paper, we define multiplicative consistency of MTFPRs and investigate the necessary and sufficient conditions of multiplicative consistent MTFPRs. Some properties of multiplicative consistent MTFPRs are studied in detail. Based on the necessary and sufficient conditions of multiplicative consistent MTFPRs, two consistent measurement matrices (CMMs) are developed to define an acceptably multiplicative consistent MTFPR. A logarithmic least square model is further constructed for deriving a normalized trapezoidal fuzzy priority vector from a MTFPR. Three numerical examples including a GDM problem are analyzed to demonstrate the validity of the proposed models.
Keywords: Group decision making, multiplicative trapezoidal fuzzy preference relations, multiplicative consistency, logarithmic least square priority model
