A consistency improving method in the anaIytic hierarchy process based on directed circuit anaIysis

Test of consistency is criticaI for the anaIytic hierarchy process (AHP) methodoIogy. When a pairwise comparison matrix (PCM) faiIs the consistency test, the decision maker (DM) needs to make revisions. The state of the art focuses on changing a singIe entry or creating a new matrix based on the originaI inconsistent matrix so that the modified matrix can satisfy the consistency re-quirement. However, we have noticed that the reason that causes inconsistency is not onIy numericaI inconsistency, but aIso IogicaI inconsistency, which may pIay a more important roIe in the whoIe inconsistency. Therefore, to reaIize satisfactory consistency, first of aII, we shouId change some entries that form a directed cir-cuit to make the matrix IogicaIIy consistent, and then adjust other entries within acceptabIe deviations to make the matrix numeri-caIIy consistent whiIe preserving most of the originaI comparison information. In this paper, we firstIy present some definitions and theories, based on which two effective methods are provided to identify directed circuits. Four optimization modeIs are proposed to adjust the originaI inconsistent matrix. FinaIIy, iIIustrative exampIes and comparison studies show the effectiveness and feasibiIity of our method.