基于工业搅拌器选型的层次分析法权重计算方法

Weight Calculation Method of Analytic Hierarchy Process Based on Industrial Agitator Selection

为了应用层次分析法进行工业搅拌器选型,采用两种常用标度针对搅拌器选型实例建立比较矩阵,用4种矩阵计算方法求解权重向量,最终得到了综合权重排序,并确定了每种计算方法求解矩阵的计算机耗时。综合权重排序结果显示90/9~99/9标度法相比于1~9标度法的误差较小,较为符合实际,更适于工业搅拌器的层次分析法选型。在9^(0/9)~9^(9/9)标度下比较综合权重结果与耗时量可知,方根法(RMS)相比其他3种矩阵计算方法更适于搅拌器选型的层次分析法应用,在同样满足一致性和计算精度的基础上,其计算时间最少(效率最高),耗时分别是和积法(SPM)的2.50%、特征根法(EM)的32.36%、行和归一化法(NRA)的76.34%。

In order to apply the commonly-used scales were adop analytic hierarchy process （AHP） to select industrial agitators, two kinds of ted to establish the comparison matrix for the agitator selection and the weight vectors were solved by four matrix calculation methods to obtain the weight sequencing and the computational cost of each method. The sequencing result of comprehensive weights shows that, compared with the 1 ~ 9 scale methods, the 90/9 - 99/9 scale method has less error and it＇ s more realistic and more suitable for AHP se- lection of the industrial agitators. Comparing the results of comprehensive weights and time consumption in the 90/9 ~ 99/9 scales shows that, compared to the other three matrix calculation methods, the root mean square （RMS） method is more suitable for application of the agitator selection＇ s APH. On the basis of the same con- sistency and calculation accuracy, the calculation time of RMS is the least （i. e. the highest efficiency） and the time-consumption is 2.50% of the sum-product method （ SPM ）, 32.36% of the eigenvector method （EM） and 76.34% of the row and normalization （NRA） which shows that the RMS has the highestcalcula- tion efficiency.