A note on "A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices"
Fuzzy Sets and Systems, 2018, 341: 145-153.
A recent paper by Liu, Zhang and Zhang (2014)  introduced a consistency index of an interval multiplicative reciprocal matrix (IMRM). In the context of group decision making, each decision maker supplies an IMRM to describe its preferences. The consistency index of each IMRM is used to rank individual IMRMs. This ordering is then employed in the aggregation process which is based on an ordered weighted geometric average operator. Furthermore, these authors devised an approach to determine importance weights of individual IMRMs. This note shows that such a consistency index highly depends on the numbering of compared objects, and the determination method of importance weights is questionable. A new consistency index is defined and used to rank individual IMRMs. A novel method is developed to obtain importance weights of individual IMRMs, and some properties are provided for the aggregation operator and the aggregated group IMRM.
Group decision making; Interval multiplicative reciprocal matrix; Consistency index; Induced ordered weighted geometric averaging operator