The Properties of Consistency for the Aggregation of Individual Reciprocal Judgment Matrix
综合判断矩阵的几个性质

The aggregation of individual reciprocal judgment matrix (AIJ) has two different approaches: convex combination and hadamard convex combination of reciprocal judgment matrix. By giving a counter example, this paper points out and analyses the errors Systems Engineering - Theory & Practice, 1997(4)87,1999(4) 133, 2000(4)83,Chinese Journal of Computers, 2001(1)106] in the properties for AIJ. Moreover, we give two properties on its consistency. (i) When using the eigenvector priorization method as the priorization procedure, and the Saaty's consistency index as the inconsistency measure, the paper proves convex combination and hadamard convex combination of reciprocal judgment matrix is of acceptable consistency under the condition that all reciprocal judgement matrices given by experts for the same problem of decision-making are of acceptable compatibility. (ii) When using the row geometric mean method as the priorization procedure, and the geometric consistency index as the inconsistency measure, the paper proves that the consistency of hadamard convex combination is smaller than the largest individual inconsistency. These Properties is of importance to group decision making.