数值标度选择的一个数学实验

讨论了标度与判断矩阵不一致的关系,把判断矩阵的不一致分成矛盾不一致和标度不一致两类.通过扩展五标度等级对比判断矩阵,总共构造了75000(5!×54)个没有矛盾和逻辑错误的判断矩阵,并把他们分成54个等价类进行计算仿真,来研究由标度导致的不一致.通过比较发现9/9~9/1标度,10/10~18/2标度,指数标度的平均一致性相差不大,都比最常用的1-9标度具有明显好的一致性.

Simulation and Comparative Study on Several Scales

This paper first reveals the relation between scales and the consistency of judgement matrices.Then we construct 75000 judgement matrices that are neither random nor illogical and prove that these judgement matrices can be classified into 54 equivalents.By computing the consistency index of these judgement matrices,we find that 9/9～9/1 scale,10/10～18/2 scale and power scale are better than 1-9 scale.The result is of importance to the analytic hierarchy process.