Angle Cosine Method for Judgment Matrix Similarity in Group AHP

Abstract

Aim at the problem that the measure of judgment matrix similarity is easily affected by 1–9 division, from the perspective of “relative” similarity, four judgment matrix similarity measurement methods were proposed based on angle cosine: method one, by comparing all the experts judgment matrix measurement information, the method based on angle cosine is proposed for judgment matrix relative similarity measurement, to reduce the influence of 1–9 scale; method two at the base of method one, by introducing gray relation degree, each expert judgment matrix similarity relative value is calculated based on comparative meaning; method three at the base of method one, using D-S composition rule to fuse the measurement information of row and column of judgment matrix; method four using D-S composition rule to fuse the measurement information based on angle cosine and the measurement information based on Euclidean distance. In the example analysis, based on the consistency test index CR, the result rationality of the four method is analyzed, the analysis shows that the method three that based on multi-information fusing or the method four that based on different measurement method fusing gets result more reasonable.