基于灰色关联的决策分析.

基于灰色关联分析的决策方法引言关联分析：发现存在于大量数据集中的关联性或相关性，从而描述了一个事物中某些属性同时出现的规律和模式。灰色关联分析：以灰色系统理论为基础，引入了灰色关联度、灰色关联决策等概念关联分析法根据因素之间发展趋势的相似或相异程度，亦即“灰色关联度”，作为衡量因素间关联程度的一种方法。灰色关联分析法①•灰色关联生成②•参考序列定义③•灰色关联系数④•灰色关联度2.1灰色关联生成JI12341****2****3****表Y是原始数据表，I代表备选方案1,2,3…,J代表各个参考属性1,2,3,4….表1原始数据表（Y表）相关序列生成对于一个选项i，用表示：表示每个属性j在选项i中的数值表现通过公式Eqs.1,2,3.相关序列：),...,,...,,(21inijiiiyyyyYijyiYiYiXiX),...,,...,,(21inijiiixxxxX灰色关联生成公式Eq.(1)适用于越大越好的属性类(i=1,2,…m,j=1,2,…,n)Eq.(2)适用于越小越好的属性类(i=1,2,…m,j=1,2,…,n)},...2,1,{},...,2,1,{},...,2,1,{miyMinmiyMaxmiyMinyxijijijijij},...2,1,{},...,2,1,{},...,2,1,{miyMinmiyMaxymiyMaxxijijijijij灰色关联生成公式Eq.(3)和期望值越接近越好的属性类(i=1,2,…m,j=1,2,…,n)*yj}},...,2,1,{y,y-m}2...,1i,{y{1*ij*ijij*miyMinMaxMaxyyxijjijij，0X1.2参考序列定义=（1,1,,,1）寻找一个尽可能和接近的序列。）（njxxxxX0002010,...,,...,,0X灰色关联系数描述和的接近程度。系数越大说明越接近，计算公式Eq.(4)：(i=1,2,..,m;j=1,2,…n)jx0ijxmaxmaxmin0),(ijijjxxijojijxx},...,2,1;,...,2,1,{minnjmiMinij},...,2,1;,...,2,1,{maxnjmiMaxij]1,0[区分系数，区分系数•延伸或者压缩灰色关联系数的范围灰色关联度表示的是相关系列和参考序列的关联度Eq.(5)（i=1,2,…m）是各个属性的权重关联度最大的选项就是最合适的选择njijojjixxwXX10),(),(jw设施布局问题把一条完整的流水线分为10个部分六个属性：流水线距离；邻接得分；形状比例；灵活性；可达性；维护性。AHP程序：分析后面三个属性的估计值DistanceScoreShapeFlexAccessMainten1185.9588.280.04940.02940.0132207.3793.750.04940.01470.05193206.3887.850.0370.01470.05194189.6688.280.0370.01470.05195211.4687.710.06170.01470.0396264.0752.070.04940.01470.051972288140.02470.07350.06498185.5996.250.0370.04410.0399185.8597.850.07410.04410.051910236.1587.850.07410.05880.064911183.18820.08640.10290.090912204.18813.300.0370.05880.02613225.2688.140.02470.07350.051914202.82880.02470.05880.051915170.1498.280.08640.11760.116916216.3897.710.07410.07350.051917179.80810.300.09880.13240.090918185.751010.160.07410.05880.03918个选项灰色关联生成原始数据y--相关序列xEq.(2)距离属性Eq.(3)形状属性Eq.(1)剩下的属性对于score属性的计算，运用Eq.(1)},...2,1,{},...,2,1,{},...,2,1,{miyMinmiyMaxmiyMinyxijijijijijScore计算示例Max=10,Min=5i=1时：x=(8-5)/(10-5)=0.6i123456789101112131415161718y8988858998888899810x.6.8.6.6.60.6.8.8.6.6.6.6.6.8.8.61MinMaxMinyxTable2DistanceScoreShapeFlexAccessMainten10.83170.60.440.3330.1249020.60360.80.78850.33300.374430.61420.60.47310.16600.374440.79220.60.440.16600.374450.56010.60.48380.499300.25026000.91770.33300.374470.3840.6000.49980.499580.83550.80.59620.1660.24980.250290.83550.80.47310.6670.24890.3744100.29720.60.47310.6670.37470.4995110.86120.60.92310.83270.74940.7498120.63760.60.05380.1660.37470.1251130.41320.60.450800.49960.3744140.65210.60.461500.37470.37441510.80.440.83270.87431160.50770.80.48380.6670.49960.3744170.89720.60.2846110.7498180.833810.29540.6670.37470.2502灰色关联生成灰色关联系数Eq.(4)计算灰色关联系数例如，且设，则maxmaxmin0),(ijijjxx1683.08317.0-1111max0min5.0)15.01683.0/()15.00()(1101xx，7481.0DistanceScoreShapeFlexAccessMainten10.74810.55560.47170.42860.36360.333320.55780.71430.70270.42860.33330.444230.56440.55560.48690.37480.33330.444240.70640.55560.47170.37480.33330.444250.5320.55560.49210.49970.33330.400160.3330.33330.85870.42860.33330.444270.44800.55560.33330.33330.49980.499880.75250.71430.55320.37480.39990.400190.75250.71430.48690.60.39990.4442100.41570.55560.48690.60.44430.4998110.78270.55560.86670.74920.66610.6665120.57980.55560.34570.37480.44430.3637130.46010.55560.47650.33330.49980.4442140.58970.55560.48150.33330.44430.44421510.71430.47170.74920.7991160.50390.71430.49210.60.49980.4442170.82940.714340.4114110.6665180.750510.41510.60.44430.4001灰色关联系数关联度计算本文设置6个属性的权重都是1/6。Eq.(5)计算关联度（i=1,2,…m）•比如，njijojjixxwXX10),(),(4835.06/)3333.03636.04286.04717.05556.07481.0(),(10XX灰色关联度I1234560.48350.53020.45990.4810.46180.4552789101112130.4450.53250.56630.50040.71450.4440.461614151617180.47480.7890.54240.77030.60174种方法对比123456789101112131415161718G108151113161775931814121624D104151114618781211716131591T178151614913126511810112437S148151211181695731713101624G:GRAD:DEAT:TOPSISS:SAW例二、问题描述现在有4类房够选择，分别用a,b,c,d表示。购房者考虑五个因素，①房屋面积S(m2);②设备质量Q(水平)③环境E（水平）④单位价格P（元）⑤距单位距离L（千米）各指标权重一样，均为0.2。房屋指标量化SQEPLa11077300010b903531008c60512360020d7059310012灰关联生成y—x的转化灰关联生成SQEPLa110.28610.833b0.6000.8331c00.5100d0.20.50.5710.8330.667属性S,Q,E都是越大越好，运用公式Eq.(1)属性P,L越小越好，运用公式Eq.(2)灰关联系数Eq.(4)(i，j=1,2,3…)ijjijxx0....}3,2,1,{in,minjiMij....}3,2,1,{ax,maxjiMijmaxmaxmin0),(ijijjxx灰色关联系数通过Eq.(4)计算出灰关联系数SQEPLa110.41210.75b0.5560.3330.3330.751c0.3330.510.3330.333d0.3850.50.5380.750.6灰色关联度I关联度a0.83b0.59c0.5d0.55假设所有属性的权重都一样为1/5。关联度的顺序；abdc对于这5种属性的综合考虑，a选项是比较合适的。参考文献①YiyoKuoa,*,TahoYangb,Guan-WeiHuangb.Theuseofgreyrelationalanalysisinsolvingmultipleattributedecision-makingproblemsComputers&IndustrialEngineering55(2008)80–93②罗党,刘思峰.灰色关联决策方法研究ChineseJournalofManagementScience:1003-207(2005)01-0101-06Thankyou!