A note on “A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making”

•The consistency definition and the goal programming model proposed by Liu, Zhang, and Wang (2012) are technically wrong.•New transitivity conditions are put forward to correct errors in Liu et al. (2012).•A two-stage goal programming approach is developed to estimate missing values.

In a recently published paper by Liu et al. [Liu, F., Zhang, W.G., Wang, Z.X. (2012). A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. European Journal of Operational Research 218, 747–754], two equations are introduced to define consistency of incomplete interval multiplicative preference relations (IMPRs) and employed to develop a goal programming model for estimating missing values. This note illustrates that such consistency definition and estimation model are technically incorrect. New transitivity conditions are proposed to define consistent IMPRs, and a two-stage goal programming approach is devised to estimate missing values for incomplete IMPRs.