综合评价方法实验报告

#重庆工商大学数学与统计学院综合评价方法》实验报告实验课程：综合评价方法_指导教师：专业班级：学生姓名：学生学号：

实验报告实验项目综合评价指标重要性权数的确定实验日期2012-6-3实验地点实验目的通过本实验本要求学生掌握综合评价指标体系中各个指标重要性权数的重要意义；掌握权数确定的定性和定量技术和技能；解决实际综合评价中重要性权数确定的处理技能。实验内容根据如下资料使用变异系数法、相关系数法、熵值法和坎蒂雷方法分别确定各个指标的权数实验过程及结果：一、运用SPSS软件进行聚类分析，选取了8个指标作为反映社会发展水平的综合评价指标，建立评价体系，数据（2002年）如下表：区县每万人拥有专业技术人员数（人）X1在岗职工平均工资（元）X2农村居民人均纯收入（元）X3传染病发病率（1/10万）X4每万人拥有公共文化设施面积（平方米）X5每万人拥有在校学生人数（人）X6第三产业就业人员占全部就业人员的比重（%）X7人均GDP（元）X8万州区213.703591151802210.77175.49971632.06421.795134844涪陵区287.1285106572006321.52166.94921668.4326.815557667渝中区880.07071342613426364.63287.0181391.15476.9738723301大渡口区485.0794121993187333.2285.476191340.83345.2580222752江北区462.9508133243151308.04248.6831117.63926.0592614659沙坪坝区360.5295134553140537.39340.00982070.02941.8543715123九龙坡区546.7185123753164321.2659.411441425.00831.429718631南岸区394.0486123323263312.8259.673071536.34335.8548814250北碚区305.1769112852704233.19220.86081688.72721.919079875万盛区190.844280422524235.55171.66071479.271205697双桥区422.587714639271189.13660.08771576.31625.937515276渝北区204.7236109352622214.8985.765351342.14229.451796962巴南区220.1691100222580261.15134.22951401.43920.21326993黔江区189.2792113211580251.7119.513311884.27519.605844587长寿区195.1265113012539158.16152.38991514.87523.805687078綦江县199.006590692355390.82110.98761636.45226.609764608潼南县132.48399242283203.83274.90642208.22114.027314334铜梁县167.404189452702184.96224.52651837.60928.619116218大足县142.794388092613162.8552.910741964.10123.85955131荣昌县173.130980902555312.14100.33571723.86318.086254598璧山县156.4435109142707169.4886.261611517.27928.81896740梁平县147.941895812010139.917.6838641733.75432.384343585城口县183.2065106581468147.1930.44141566.00714.052582449丰都县129.773788801810266.478.155861562.61612.188733401垫江县114.9158100732062190.1742.902972014.42127.593823717

武隆县160.350778961802273.43130.59951529.58123.878214678忠县171.141893141822282.3565.133591826.13335.207912867开县143.218781091722295.9874.564762344.46739.483873065云阳县136.21248621155396.0351.043571945.64813.923822199奉节县112.22779405144697.95219.49982045.00420.573072788巫山县59.5656586901453149.9441.461011845.82419.031442594巫溪县129.167675381370187.8236.020211813.28822.321711934石柱县108.198290411439111.2791.216221888.8299.7108742899秀山县143.061694611449135.1249.244532045.76515.317232742酉阳县143.247986821403185.1556.410262138.6517.7371811彭水县117.2501100831537219.0631.162041926.2910.406092694江津市136.639798722667125.2515.82841337.62828.312496887合川市136.831894602625151.4160.745551519.30330.772866377永川市176.047810811268597.9777.519461621.73427.218686697南川市146.695287472243225.3120.38231561.70118.010756145二、确定权数（一）变异系数法：过程：将数据输入excel中，对每一项指标求平均数（average）、标准差（stdev）,变异系数=标准差/平均数，得到变异系数的值以后再对变异系数进行归一化处理，即变异系数权数=每一个指标的变异系数/所有指标变异系数之和，使得所有变异系数权数之和=1，得到如下结果：指标X1X2X3X4X5X6X7X8平均值223.1273101282504.5223.88124.92931705.56825.6286971标准差（Si）155.75841726.71867.295.041119.7317274.581711.765985547变异系数（Vi）0.698070.17050.74550.42450.9583960.1609910.4591060.796归一化处理0.1581920.03860.16890.09620.2171850.0364830.104040.18分析：变异系数法是根据各个评价指标数值的变异程度来确定评价指标的权数值的方法，变异系数越大，说明该指标在这项评价上的分辨信息越丰富，因而应该给该指标以较大的权数，从变异系数的值来看，每万人拥有公共文化设施面积（X5）0.939227为最大，因此赋值最大0.215658。（二）熵值法：过程及结果：1、由于传染病发病率（X4）为逆指标，需用公式yi=1/Xi进行正向化处理，然后对各个指标值求和，结果如下：2、对指标实际值按比重法转换成评价值，即用每一个指标除以相应的指标总值，得bij3、再对bij中每一个值取对数，得ln（bij）,然后将得到的bij和ln（bij）的值对应相乘，得bij*ln（bij）,4、对每一指标的bij*ln（bij）求和得bj,对bj取绝对值，找出bj绝对值中的最大值（max）,得到系数k,即bj绝对值最大值的倒数5、计算第j项指标的熵值ej；6、归一化处理，ej/ej之和j=1、2、3、4、5、6、7、8实验结果如下：亦-3.50847-3.67517-3.5355-3.59847-3.34686-3.67628-3.60087-3.43574Bj的绝对彳3.5084673.675173.5354973.598473.3468633.6762833.6008683.435738max3.676283K0.272014ej0.9543520.9996970.9617040.9788340.91039310.9794860.934569dj0.0456480.0003030.0382960.0211660.08960700.0205140.065431wj0.1624690.0010780.1363010.0753340.31892500.0730120.232881

分析：根据熵值的特性，我们可以通过计算熵值来判断一个事件的随机性及无序程度，也可以用熵值来判断某个指标的离散程度，指标的离散程度越大，该指标对综合评价的影响越大。三、综合评价（一）综合指数评价法：用40个区县的各指标的平均值作为各项指标的评价标准，根据公式z=fw许得出以下计ixi-1io算结果并进行排名。区县综合指数排名区县综合指数排名渝中区3.2424231南川市0.83618121双桥区1.9933712武隆县0.81905922沙坪坝区1.8380663合川市0.80487323大渡口区1.7359294开县0.76574224江北区1.612355大足县0.75183125九龙坡区1.5799336忠县0.74961626南岸区1.3655357江津市0.74460127北碚区1.2484178奉节县0.7398228涪陵区1.1021259黔江区0.67747329铜梁县1.0445610垫江县0.66466730巴南区0.98270411丰都县0.65729131潼南县0.96425112梁平县0.6237332长寿区0.95995413酉阳县0.55698233万盛区0.94907214秀山县0.54869234綦江县0.93278315石柱县0.54456235渝北区0.92681516城口县0.54297236万州区0.8904617彭水县0.53286737璧山县0.87418618巫溪县0.52801138荣昌县0.85133519云阳县0.51187539永川市0.83973220巫山县0.48617440分析：由上表可知，2002年重庆社会发展水平排名前三位的分别是渝中区、双桥区和沙坪坝区，社会发展水平排名后三位的分别是巫山县、云阳县和巫溪县；发展水平最高的是主城及周边区县，发展水平低的是三峡库区及渝东南区县；总体趋势是：离主城区越远，社会发展水平越低。二）秩和比评价法：1、等级化处理，得到下表数据。区县每万人拥有专业技术人员数（人）在岗职工平均工资（元）农村居民人均纯收入（元）传染病发病率（1/10万）每万人拥有公共文化设施面积（平方米）每万人拥有在校学生人数（人）第三产业就业人员占全部就业人员的比重（%）人均GDP（元）万州区112628209222521涪陵区91525361120169

渝中区1313833611大渡口区37337213822江北区44532540186沙坪坝区726402435九龙坡区25435283483南岸区66234272857北碚区810924719248万盛区1538192510332819双桥区5171124194渝北区1211142120371012巴南区1018162713352711黔江区168312638122925长寿区149181212322210綦江县1327203916211723潼南县33192119423626铜梁县212910156141217大足县293115133082120荣昌县1937173317183124璧山县231281419311114梁平县24212484017728城口县171434937253537丰都县3430272822263829垫江县371723183371427武隆县2239282914292022忠县202526302515632开县27363031241430云阳县32353223193738奉节县3824373862633巫山县4033351034133036巫溪县3540401735162339石柱县392838518114031秀山县28223673253434酉阳县263439162933340彭水县3616332236103935江津市312012639391313合川市302313112630916永川市181311423231515南川市25322223152732182、确定权数，由上文可知：w0.158190.038640.168950.09620.217190.036480.104040.18032

3、求秩和比，公式为：z=空fwr,得到下表数据:inpjijjT区县秩和比位次区县秩和比位次渝北区1.8435071酉阳县6.83466121沙坪坝区1.9837432巫溪县6.85574522北碚区2.4501073綦江县6.92770823大渡口区3.1907274潼南县6.99486124江北区3.5397675忠县7.07928825铜梁县3.6356866奉节县7.43113126九龙坡区4.1397687垫江县7.52814327南岸区4.2055078南川市7.66157828合川市4.2820839梁平县7.7460329巴南区4.56987210武隆县8.08590630永川市4.87704511涪陵区8.37332931彭水县4.90395112丰都县8.81697932江津市4.91461813荣昌县8.96940833渝中区5.03011814秀山县9.01103734璧山县5.14712815大足县9.09412435双桥区5.79503716开县9.30489936长寿区5.99092617城口县9.56517137巫山县6.07863118黔江区9.98405438万州区6.37109219云阳县10.1740239万盛区6.47046120石柱县10.3393540分析：由上表可以看出，2002年重庆社会发展水平排名前三位的是渝北区、沙坪坝区和北碚区，排名后三位的分别是黔江区、云阳县和石柱县；排名靠前的是主城及周边区县，大致上为离主城区越远，社会发展水平越低。（三）功效系数评价法：1、由于X4经过转换后均为正指标，取最大值和最小值分别为满意值、不允许值如下表：满意值880.070714639134260.01122660.08772344.46776.9738723301不允许值59.56565753813700.0018617.6838641117.6399.7108741811差值820.5057101120560.009359652.40391226.82867.263214902、由功效函数d=xi7；X40+60，计算各指标的功效系数。ix（h）—x（s）ii每万人拥第三产业每万人拥每万人拥在岗职工农村居民传染病发有公共文就业人员A-kh区县有专业技平均工资人均纯收病率（1/10化设施面有在校学占全部就人均术人员数生人数GDP（兀）（元）入（元）万）积（平方业人员的（人）（人）米）比重（%）万州区67.5142968.8832661.4333172.3250370.2890876.7725367.1862765.64542

涪陵区71.093877.5693662.1101565.3399669.7648377.9582370.1718270.89995渝中区10093.1671610063.7682977.1264568.9178100100大渡口区80.7439986.2554666.0285364.8732164.7695867.2771281.139298.97813江北区79.6652192.5925965.9090965.9216974.776076069.7220783.91438沙坪坝区74.6721393.3305265.872596080.3754791.0521279.1151284.77804九龙坡区83.7489387.2468765.9522265.3507263.1715170.021672.9157791.30758南岸区76.306287.0046566.2806965.7096763.1875573.6516175.5473383.15309北碚区71.9736681.1068964.4260170.3753673.0702478.6267.2599875.00977万盛区66.3998962.8390463.828870.1917270.053771.7907966.1187467.23313双桥区77.6974910064.4492410010074.9548969.6496685.06282渝北区67.0765279.1353364.1539571.9362464.7873167.319871.7395469.58772巴南区67.8294973.992464.014668.4129967.7587369.2531366.2455369.64542黔江区66.3235981.3096760.6967569.0267960.7252884.995765.8843565.16705长寿区66.6086681.1970163.8785779.0704168.8721772.9516468.3819169.80363綦江县66.7978168.6241463.2680862.9827966.3337376.9155970.0494465.20614潼南县63.5547673.4403663.029273.0154776.3838795.5577962.566964.69614铜梁县65.2571767.9256464.4193875.1547673.2949983.4742171.2443668.20289大足县64.0574467.1595564.1240978.2921362.7729487.5983968.4139166.17962荣昌县65.5363663.1094263.9316565.7394465.6806479.7655964.9806865.18753璧山县64.7228479.0170464.4359777.2654264.8177473.0300471.3631769.1745梁平县64.3083871.5082462.1234282.595426080.0880773.4834763.302城口县66.0275577.5749960.3251581.0844861.395374.6187862.5819361.18753丰都县63.4226767.559561.4598568.0904664.3207674.5082161.4735362.95952垫江县62.6983574.2796862.2959574.5216762.1593489.2390570.6346463.5477武隆县64.9133262.0166261.4333167.6779667.5361773.4311468.4250465.33644忠县65.4393970.0042261.4996767.1841363.5223483.1000375.1625961.96557开县64.0781263.2164561.1678866.4870464.1005810077.7054262.33411云阳县63.7365666.1005560.6071796.5544262.6584686.9967462.5053660.7222奉节县62.567370.5168360.2521695.6819972.986890.2361966.4595361.81852巫山县6066.4892360.2753880.551962.0709383.7420565.5427661.45742巫溪县63.39313606074.8028861.7373582.6812267.4994260.22894石柱县62.3708668.4664160.2289390.4584565.1215185.144196062.02513秀山县64.0704770.8322860.2621183.6783862.5481690.2610163.3339961.7329酉阳县64.0795566.4441660.1094975.1310462.987593.2894464.7729860彭水县62.8121474.3360160.5540871.5576261.4394986.3655960.4134361.64356江津市63.7573973.1474464.3032586.1710460.4993667.1726371.0620269.44812合川市63.7667670.8266464.163980.2751563.253373.0960272.5251568.49884永川市65.6785678.4368464.3629795.6730864.2817476.4357270.4115569.09