数模模糊数学作业题目答案

1、（模糊聚类）已知我国31个省农业生产条件的5大指标数据。五大指标的数据省份X1X2X3X4X5省份X1X2X3X4X5北京0.612.493.811.371.16湖北0.970.560.691.221.57天津0.692.734.381.061.16湖南1.050.800.330.851.25河北0.882.331.411.140.94广东0.821.052.611.241.99山西0.951.331.100.820.49广西1.100.700.300.930.81内蒙古1.210.650.680.470.18海南1.140.660.140.791.15辽宁0.981.082.191.211.17重庆1.010.490.420.750.60吉林1.180.700.801.080.52四川1.030.530.450.820.76黑龙江1.190.540.630.520.36贵州1.180.380.170.560.24上海0.500.875.941.402.96云南1.230.730.340.630.43江苏0.791.102.231.591.40西藏1.301.380.070.450.34浙江0.731.572.270.902.03陕西1.080.680.811.060.27安徽1.041.030.351.130.99甘肃1.070.810.670.640.33福建0.920.921.161.622.29青海1.181.350.270.480.38江西0.980.460.470.751.10宁夏1.131.170.871.080.18山东0.971.731.041.412.09新疆1.280.771.480.880.45河南1.091.350.611.200.90（1）作聚类图。并告知分5类时，每一类包含的省份名称（列表显示）。（2）若分为3类，问相似水平（就是阈值）不能低于多少？解：新建data.txt,将全部数据存入该data.txt,打开MATLAB,在命令窗口输入：datastruct=importdata('data.txt')检查一下数据是否导入正确：datastruct.data%这里是31*5的数值矩阵datastruct.textdata%这里是31*1的省名称文本矩阵fuzzy_jlfx(3,5,datastruct.data)%调用网站所给的模糊数学聚类程序包9311.000.830.67170.931150.912130.913290.914260.905110.896190.897100.89860.889310.8810160.8811120.8712210.8713180.8714230.8515220.8516200.8517140.8418300.8319270.832070.8321280.8222250.8223240.812480.802550.792640.792730.762820.742910.6730根据编号代表意义，可知分5类时的省份编号为：第一类：9、上海第二类：1、北京2、天津第三类：3、河北第四类：4、山西第五类：其余省市自治区都属于第五类（2）若分成3类，由聚类图可知阈值应在（0.74,0.76）内。2、（模糊评价）对某水源地进行综合评价，取U为各污染物单项指标的集合，取V为水体分级的集合。可取U(矿化度，总硬度，NO3-，NO2-，SO42-)，V（I级水，Ⅱ级水，Ⅲ级水，Ⅳ级水，V级水）。现得到该水源地的每个指标实测值x，计算得到对于I~V级水的隶属度：I级水Ⅱ级水Ⅲ级水Ⅳ级水V级水矿化度00.350.6500总硬度0.510.49000硝酸盐0.830.17000亚硝酸盐000.9250.0750硫酸盐0.210.79000可以根据水质对污染的影响计算权重为A=（0.28,0.22,0.06,0.22,0.22）,试判断该地水源是几级水？解：在matlab命令窗口内输入数据：V=[00.350.6500;0.510.49000;0.830.17000;000.9250.0750;0.210.79000];A=[0.28,0.22,0.06,0.22,0.22];fuzzy_zhpj(2,A,V)%调用网站所给的模糊综合评判程序包ans=0.11220.17380.20350.01650所以可以判断该地水源是Ⅲ级水。3、（模糊识别）现有茶叶等级标准样品五种：EDCBA，其中放映茶叶质量的因素论域为U，滋味香气汤色净度色泽条索U。假设各个等级的模糊集为：)4.05.06.03.04.05.0(A)2.02.01.02.02.03.0(B)2.01.01.02.02.02.0(C)1.01.01.02.01.00(D)1.01.01.01.01.00(E现有一样品，其模糊集为：)6.05.04.01.02.04.0(L，试依据择近原则确定该样本属于哪一等级。解：在matlab命令窗口内输入数据：V=[0.50.40.30.60.50.4;0.30.20.20.10.20.2;0.20.20.20.10.10.2;00.10.20.10.10.1;00.10.10.10.10.1];L=[0.40.20.10.40.50.6];fuzzy_mssb(1,V,L)%调用网站所给的模糊识别程序包ans=0.68970.47830.39130.21740.2273由择近原则可知，该样品属于A等级。4、（模糊线性规划）试求解43211081512maxxxxxZ12341234123412341.21.41.5[2100,100]0.50.60.60.8[1000,50].0.70.70.80.8[1300,50],,,0xxxxxxxxstxxxxxxxx解：首先求解普通线性规划：43211081512maxxxxxZ0,,,13008.08.07.07.010008.06.06.05.021005.14.12.1..4321432143214321xxxxxxxxxxxxxxxxts用LINGO编写代码，得到Globaloptimalsolutionfound.Objectivevalue:24428.57Totalsolveriterations:4VariableValueReducedCostX11142.8570.000000X2714.28570.000000X30.0000006.571429X40.00000010.57143再解带伸缩指标的普通线性规划：43211081512maxxxxxZ0,,,12508.08.07.07.010508.06.06.05.022005.14.12.1..4321432143214321xxxxxxxxxxxxxxxxts解得：Globaloptimalsolutionfound.Objectivevalue:26142.86Totalsolveriterations:4VariableValueReducedCostX1214.28570.000000X21571.4290.000000X30.0000006.571429X40.00000010.57143最后添加，求解普通线性规划：max0,,,1250508.08.07.07.01050508.06.06.05.022001005.14.12.157.24428)(1081512..4321432143214321124321xxxxxxxxxxxxxxxxffxxxxts解得：Objectivevalue:0.4999998Totalsolveriterations:4VariableValueReducedCostLAMDA0.49999980.000000X1678.57120.000000X21142.8570.000000X30.0000000.1916664E-02X40.0000000.3083329E-02代入求得最优值为25285.71