A consistency model for group decision making problems with interval multiplicative preference relations

• Construct referenced consistent IMPR (RCIMPR) and define consistency level for IMPR.
• Propose algorithm to improve consistency level for unacceptable consistent IMPR.
• Collective RCIMPR is the weighted geometric average of individual RCIMPRs.

The main aim of this paper is to present a consistency model for interval multiplicative preference relation (IMPR). To measure the consistency level for IMPR, a referenced consistent IMPR of a given IMPR is defined, which has the minimum logarithmic distance from the given IMPR. Based on the referenced consistent IMPR, the consistency level of an IMPR can be measured and an IMPR with unacceptable consistency can be adjusted by a proposed algorithm such that the revised IMPR is of acceptable consistency. A consistency model for group decision making (GDM) problems with IMPRs is proposed to obtain the collective IMPR with highest consistency level. Numerical examples are provided to illustrate the validity of the proposed approaches in decision making.

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