Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices

Missing values and inconsistency of pairwise comparison matrices (PCM) in AHP are tackled with different methods in extant studies. In this article, we prove that connecting path method (CPM), which is a well-known approach of estimating missing judgments, also guarantees minimal geometric consistency index, and only involves elementary connecting paths by unraveling its connection with logarithmic least square method. The formal proofs suggest that CPM alone is sufficient to fix both missing judgments and inconsistency of PCM in AHP. Based on this well grounded merit, a procedure is proposed to improve consistency for incomplete PCM. The validity of the proposed procedure is illustrated by classical examples, and its advantages over other consistency improving approaches are also discussed in detail.