Comments on “A group decision-making model with interval multiplicative reciprocal matrices based on the geometric consistency index”

Abstract

Abstract A very recent paper published by Liu et al. [Liu, F., Zhang, W. G., & Shang, Y. F. (2016). A group decision-making model with interval multiplicative reciprocal matrices based on the geometric consistency index. Computers & Industrial Engineering, 101, 184–193.] defined a geometric consistency index (GCI) to measure the inconsistency level of an interval multiplicative reciprocal matrix (IMRM) and to devise a GCI induced ordered weighted geometric averaging (GCI-IOWGA) operator, and proposed a method for determining the associated weight vector of the GCI-IOWGA operator. This note reveals that such a GCI and the GCI-IOWGA operator as well as the associated weight determination method are questionable. A new consistency index called a weak GCI and an associated weight determination approach are put forward to rectify defects in the existing results. A notion of acceptably weak consistency of IMRMs is introduced to develop a weak GCI induced IMRM ordered weighted geometric averaging operator for aggregating individual IMRMs with acceptably weak consistency. Some important properties are explored for the proposed weak GCI and the weak GCI induced aggregation operator.