基于主成分融合熵值法的综合评价模型

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1、基于主成分分析和爛值法的综合评价模型1.设原始变量X

2、,X2，...,Xp的n次观测数据矩阵为:2•将数据矩阵按列进行中心标准化。为了方便，将标准化后的数据矩阵仍然记为X。3•求相关系数矩阵R,R=(讥加©的定义为:其中,4.求/?的特征方程det(/?-2E)=0的特征根人泌》¥〉0。并计算方差的贡献率q,其中5.确定主成分个数刃:>a,Q根据实际问题确定，一般取80%o6.计算刃个相应的单位特征向量:0严021■•■,02='Pn022■•■，…,0加=「0匚■•■几2_7.计算主成分:Fi=际X±+阻已+—卜8諮

3、卩(i-1,2,…,m)&逻辑评分函数scoredj)=—G(m)(l+e^J)当F与评分止相关时取负，当F与评分负相关时取止。9.炳值法确定权重第j个纬度的嫡值计算公式：Hj=-贾齐何馆)Inn客户信用度与各相关变量之间并不是单纯的线性关系，因此为了消除主成分的简单相加带来的负面影响，采用逻辑函数对选取的几个主成分再进行累计，计算得出第i个样木的j纬度的故终得分：Cj其中scores计算伽权削，吹民实际例子:1•数据namesXIOOoLong,jumpShot,putHigh.jumpX400nXllOm.hur(

4、DiscusPole.vault

5、javelineX1500mRankPointsCoffipetitioSEBRLE11.047.5814.832.0749.8114.6943.755.0263.19291.718217DecastarCIAI10.767.414.261.8649.3714.0550.724.9260.15301.528122DecastarBERNARD11.027.2314.251.9248.9314.9940.875.3262.77280.148067DecastarTURKOV11.347.

6、0915.192.150.4215.3146.264.7263.44276.458036DecastarZSIVOCZKY11.137.313.482.0148.6214.1745.674.4255.3726878004DecastarMcMullen10.837.3113.762.1349.9114.3844.414.4256.37285.187995DecastarMAKTIHEAU11.646.8114.571.9550.1414.9347.64.9252.33262.197802DecastarHEW11.37

7、7.5614.411.8651.115.0644.994.8257.19285.1107733DecastarBARRAS11.336.9714.091.9549.4814.4842.14.7255.4282117708DecastarNOOL11.337.2712.681.9849.215.2937.924.6257.44266.6127651DecastarBOURGUIGW11.366.813.461.8651.1615.6740.495.0254.68291.7137313DecastarSebrle10.85

8、7.8416.362.1248.3614.0548.72570.52280.0118893OlympicGClay10.447.9615.232.0649.1914.1350.114.969.7128228820OlympicGKarpov10.57.8115.932.0946.8113.9751.654.655.5427&1138725OlympicGMacey10.897.4715.732.1548.9714.5648.344.45&46265.4248414OlympicGVarners10.627.7414.4

9、81.9747.9714.0143.734.955.39278.0558343OlympicGZsivoczky10.917.1415.312.1249.414.9545.624.763.45269.5468287OlympicGHernu10.977.1914.652.0348.7314.2544.724.857.76264.3578237OlympicGBernard10.697.4814.82.1249.1314.1744.754.455.27276.3198225OlympicGSchrarzl10.987.4

10、914.011.9449.7614.2542.435.156.32273.56108102OlympicGPogorelov10.957.3115.12.0650.7914.2144.6553.45287.63118084OlympicGSchoenbecl10.97.314.771.8850.314.3444.41560.892