On consistency of the weighted geometric mean complex judgement matrix in AHP
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TL;DR
It is proved that the weighted geometric mean complex judgement matrix (WGMCJM) is of acceptable consistency and a theoretic basis has been developed for the application of the WGMM in group decision making.
Abstract
The weighted geometric mean method (WGMM) is the most common group preference aggregation method in the Analytic Hierarchy Process. This paper reports on research concerning the consistency of WGMM and proves that the weighted geometric mean complex judgement matrix (WGMCJM) is of acceptable consistency. In Saaty's (T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980) opinion, a consistency ratio (CR) of 0.1 or less is acceptable under the condition that all judgement matrices given by experts for the same problem of decision-making are of acceptable consistency. Accordingly, a theoretic basis has been developed for the application of the WGMM in group decision making.