模糊综合评价法举例
例：运用现代物流学原理，在物流规划过程中，物流中心选址要考虑许多因素。根据因素特点划分层次模块，各因素又可由下一级因素构成，因素集分为三级，三级模糊评判的数学模型见表2所示：
表2 物流中心选址的三级模型
因素集U 分为三层：
第一层为 {}12345,,,,U u u u u u =
第二层为 {}{}{}111121314441424344551525354,,,;,,,;,,,u u u u u u u u u u u u u u u === 第三层为 {}{}5151151251352521522,,;,u u u u u u u ==
假设某区域有8个候选地址，决断集{},,,,,,,V A B C D E F G H =代表8个不同的候选地址，数据进行处理后得到诸因素的模糊综合评判如表3所示。
表3 某区域的模糊综合评判
⑴ 分层作综合评判
{}51511512513,,u u u u =，权重{}511/3,1/3,1/3A =，由表3对511512513,,u u u 的模糊
评判构成的单因素评判矩阵：
510.600.710.770.600.820.950.650.760.600.710.700.600.800.950.650.760.910.900.930.910.950.930.810.89R ⎛⎫ ⎪= ⎪ ⎪⎝⎭
用模型(,)M ∙+（矩阵运算）计算得：
515151(0.703,0.773,0.8,0.703,0.857,0.943,0.703,0.803)B A R ==
类似地：525252(0.895,0.885,0.785,0.81,0.95,0.77,0.775,0.77)B A R ==
5550.7030.773
0.80.7030.8570.9430.7030.8030.8950.8850.7850.810.950.770.7750.77(0.40.30.20.1)0.810.940.890.600.650.950.950.890.900.600.920.600.600.840.650.81B A R ⎛⎫ ⎪
⎪== ⎪ ⎪⎝⎭
=(0.802,0.823,0.826,0.704,0.818,0.882,0.769,0.811)
4440.600.950.600.950.950.950.950.950.60
0.690.920.920.870.740.890.95(0.10.10.40.4)0.950.690.930.850.600.600.940.780.75
0.600.800.930.840.840.600.80B A R ⎛⎫
⎪
⎪== ⎪
⎪
⎝⎭
=(0.8,0.68,0.844,0.899,0.758,0.745,0.8,0.822)
1110.910.850.870.980.790.600.600.950.93
0.810.930.870.610.610.950.87(0.250.250.250.25)0.880.820.940.880.640.610.950.910.90
0.830.940.890.630.710.950.91B A R ⎛⎫
⎪
⎪== ⎪
⎪
⎝⎭
=(0.905,0.828,0.92,0.905,0.668,0.633,0.863,0.91)
（2）高层次的综合评判
{}12345,,,,U u u u u u =，权重{}0.1,0.2,0.3,0.2,0.2A =，则综合评判
12345B B B A R A B B B ⎛⎫ ⎪ ⎪
⎪
== ⎪ ⎪ ⎪⎝⎭
0.9050.8280.920.9050.6680.6330.8630.910.950.900.90.940.600.910.950.94 =(0.10.20.30.20.2)0.900.900.870.950.870.650.740.610.80.680.8440.8990.7580.7450.80.8220.8020.8230.8260.7040.8180.8820.7690.811⎛ ⎝ ⎫⎪⎪
⎪
⎪
⎪ ⎪⎭
=(0.871,0.833,0.867,0.884,0.763,0.766,0.812,0.789)
由此可知，8块候选地的综合评判结果的排序为：D,A,C,B ,G,H,F,E ，选出较高估计值的地点作为物流中心。
应用模糊综合评判方法进行物流中心选址，模糊评判模型采用层次式结构，把评判因素分为三层，也可进一步分为多层。这里介绍的计算模型由于对权重集进行归一化处理，采用加权求和型，将评价结果按照大小顺序排列，决策者从中选出估计值较高的地点作为物流中心即可，方法简便。
