综合评价实验报告

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方法及应用实验日期2013-6-8实验地点80806实验目的1、 掌握综合评价指标体系建立的操作技术和技能；掌握综合评价指标体系的定性分析和定量分析方法的实际应用2、 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。3、 通过本实验要求学生掌握各种综合评价的综合方法实际应用和计算过程；掌握各种综合评价方法的特点和不足。实验内容根据实验所给的数据资料，选取所需的综合评价方法分析重庆市各区县的社会发展状况，并提出相关的建议。实验过程及结果:一、数据的初步处理:1、在原始数据中选出重庆市各区县2003的数据。并作整理，部分结果显示如下:区县人口出生£每万人拥;人均图书4在校中小巴每万人拥有专业技术人员数（人城镇居民,农村居或在岗职工3农村居民/农村改水］重庆市9.585019140.2593.8223.3741重庆市25.7231.4512440221590.43万州区11.1363416.225490.12383896216.4763万州区22.5132.510389192574.68涪陵区8.06895716.802140.34280390.1280.0555涪陵区25.9333.311896215399.89渝中区4.89921348.803764.50073295.3874.4899渝中区23.0823.08154931549399.89大渡口匚7.00478720.644910.17931695.8475.58大渡口［24.5941.316984338292.2江北区7.69607425.147980.17917198.3437.1781江北区24.8531.315042335699.73沙坪坝E7.07303815.684150.20784193338.7221沙坪坝［19.9235.315154333499.19九龙坡匚7.73688720.336930.13780498.2579.3107九龙坡匚23.542.713696335698.47南岸区7.11773218.537570.05497391.8415.3726南岸区25.533714051347599.58北碇区6.06495115.679981.2421693.3289.7965北碇区19.8833.912947287599.7万盛区8.4304315.059020.17953292.7205.6166万盛区13.735.89067264599.08双桥区12.4716812.173910.07065292.7441.5217双桥区27.923815174286999.58渝北区10.722299.7092290.19558894.3204.6903渝北区46.3536.913071277795.88巴南区7.53109814.487280.11606792.7213.6684巴南区16.9833.811297271599.97黔江区13.61749.4647370.19526896183.7354黔江区35.12913747171653.49长寿区8.8778313.169550.12350798.4187.2735长寿区26.2639.512570267999.34暴江县8.83980712.495510.08440194.4192.0886秦江县21.929.410487247399.44潼南县9.3034229.5131820.10880296.9127.4376潼南县24.52911006244298.94铜梁县6.27767117.064070.10626492.7184.3633铜梁县38.53379422286799.59大足县6.1583798.8665450.11621896137.1899大足县21.0134.49906275276.17荣昌县10.3419414.318420.13302791.4195.5732荣昌县34.5629.19361268899.94璧山县6.75237811.950550.11773997.2174.2739璧山县38.6634.512143287599.84梁平县8.7262949.2826420.02710692.7131.1641梁平县15.3336.910478213576.08城口县9.43691313.118940.01783671201.1741城口县25.562610974156947.54丰都县13.292767.5268820.06144482.6129.1398丰都县32.613210953192596.08垫江县13.7503910.326090.04378492.7143.8995垫江县21.937.211163222398武隆县10.5724311.806540.20540595.7168.6486武隆县26.2532.78774194281.69忠县8.78005911.031080.03934992.7164.906忠卜县18.2330.610180192987.02开县14.3485311.675560.15625198.9112.2266开县37.8734.59030185193.78云阳县11.5658310.361680.03152894.2148.4262云阳县20.9931.89205168481.46奉节县11.408856.5214890.08411192.8121.2236奉节县30.9726.510057159092.27巫山县12.327217.6450780.00990397.349.79204巫山县33.0129.29628158592.19巫溪县8.6094728.3407470.04589694.3141.3923巫溪县20.5428.88339148576.57石柱县12.1657911.964450.11390289.8113.4913石柱县26.5331.89745158661.21二、指标赋权指标的重要性赋权就是指对于评价指标体系中的各个指标进行综合评价时，各个指标对于研究目的的影响程度是不同的。这种不同体现为重要性，将这种重要性以数量值反应出来称为赋权。确定权数的方法有很多，但从大范围上看，可以分为两大类：主观赋权法和可观赋权法。根据本实验

数据的特性和便利性，本实验采用客观赋权法中的变异系数法和熵值法。1、变异系数法变异系数方法是指根据各个评价指标数值的变异程度来确定评价指标权数值的方法。步骤：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：指标名称平均值标准差变异系数变异系数归一化处理人口出生率（％）9.5202112.828090.2970620.016767893每万人拥有执业医师助理执业医师（人）13.4218176.969650.5192780.02931107人均图书拥有量（册）0.25092350.705982.8135360.1588123在校中小学生体育锻炼达标率（%）93.0707325.230590.05620.003172267每万人拥有专业技术人员数（人）227.72673153.9110.675860.038149459城镇居民人均居住面积 。26.3065857.322510.2783530.015711845农村居民人均住房使用面积（平方米）32.9519514.421830.134190.007574482在岗职工平均工资（元）11405.1462135.330.1872250.010568054农村居民人均纯收入（元）2685.65852137.90.7960450.044933396农村改水累计受益率（%）90.00926813.66660.1518350.0085704551专染病发病率（1/ioTT）236.993991.65730.386750.021830401新生儿死亡率（％）8.76853663.981590.4540770.025630739电视人口覆盖率（%）95.5117074.719290.0494110.002789024每万人拥有公共文化设施面积（平方米）126.69846113.980.8996130.050779406城市基础设施投资占全社会固定资产投*10.3762667.302890.7038070.039726941城镇居民人均公共绿地面积（平方米）3.11975612.387450.7652690.043196259城镇生活污水处理率0020.51470618.62550.907910.051247725每万人拥有在校学生人数（人）1970.4426318.3490.1615620.009119511享受低保人数占救济对象总人数的比重（48.20435827.20520.5643710.031856408全社会保障支出占财政总支出的比重（%）16.7978795.647450.33620.018977109每万人律师拥有人数（人）1.0541072.603912.4702520.139435385登记失业率（%）4.0024391.012540.2529820.01427975每万人治安案件发案率（件/万人）36.17119925.45710.7037960.03972632第三产业就业人员占全部就业人员的比暨26.1154312.54760.4804660.027120312社会事业支出占财政总支出的比重农）54.00512212.73270.2357690.013308145非农业人口占总人口的比重很）27.30631623.3460.8549660.048259279环境保护投入占GDP的比重（%）2.14492442.094120.9763120.055108747人均GDF（元）7971.09764806.640.6030090.034037319分析：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，人均拥有量书册的变异系数值最大，因此赋值最大0.15881232、熵值法：熵值法：是根据熵值的原理和计算公式来确定指标的重要性权数的方法。过程及结果：1、采用倒数法对逆向指标正向化，部分结果显示如下：

重庆市0.104329140.2593.8223.3741重庆市25.7231.4512440221590.43万州区0.08979616.225490.12383896216.4763万州区22.5132.510389192574.68涪陵区0.12393216.802140.34280390.1280.0555涪陵区25.9333.311896215399.89渝中区0.20411448.803764.50073295.3874.4899渝中区23.0823.0S154931549399.89大渡口E0.1427620.644910.17931695.8475.58大渡口[24.5941.316984338292.2江北区0.12993625.147980.17917198.3437.1781江北区24.8531.315042335699.73沙坪坝10.14138215.684150.20784193338.7221沙坪坝[19.9235.315154333499.19九龙坡匚0.12925120.336930.13780498.2579.3107丸龙坡L23.542.713696335698.47南岸区0.14049418.537570.05497391.8415.3726南岸区25.533714051347599.58北碇区0.16488215.679981.2421693.3289.7965北暗区19.8833.912947287599.7万盛区0.11861815.059020.17953292.7205.6166万盛区13.735.89067264599.08双侨区0.08018212.173910.07065292.7441.5217双桥区27.923815174286999.58渝北区0.0932649.7092290.19558894.3204.6903渝北区46.3536.913071277795.88巴南区0.13278314.487280.11606792.7213.6684巴南区16.9833.811297271599.97黔江区0.0734359.4647370.19526896183.7354黔江区35.12913747171653.49长寿区0.1126413.169550.12350798.4187.2735长寿区26.2639.512570267999.34暴江县0.11312512.495510.08440194.4192.0886秦江县21.929.410487247399.44潼南县0.1074879.5131820.10880296.9127.4376潼南县24.52911006244298.94桐梁县0.15929517.064070.10626492.7184.3633铜梁县38.53379422286799.59大足县0.162388.8665450.11621896137.1899大足县21.0134.49906275276.17荣昌县0.09669414.318420.13302791.4195.5732荣昌县34.5629.19361268899.94璧山县0.14809611.950550.11773997.2174.2739璧山县38.6634.512143287599.84梁平县0.1145969.2826420.02710692.7131.1641梁平县15.3336.91047S213576.08城口县0.10596713.118940.01783671201.1741城口县25.562610974156947.54丰都县0.0752297.5268820.06144482.6129.1398丰都县32.613210953192596.08垫江县0.07272510.326090.04378492.7143.8995垫江县21.937.211163222398武隆县0.09458611.806540.20540595.7168.6486武隆县26.2532.78774194281.69忠县0.11389411.031080.03934992.7164.906忠卜县18.2330.610180192987.02开县0.06969411.675560.15625198.9112.2266开县37.8734.59030185193.78云阳县0.08646210.361680.03152894.2148.4262云阳县20.9931.S9205168481.46奉节县0.0876516.5214890.08411192.8121.2236奉节县30.9726.510057159092.27巫山县0.0811217.6450780.00990397.349.79204巫山县33.0129.29628158592.19巫溪县0.1161518.3407470.04589694.3141.3923巫溪县20.5428.88339148576.57石柱县0.08219811.964450.11390289.8113.4913石柱县26.5331.89745158661.21秀山县0.0566587.8895070.07415188.7146.8203秀山县32.6326.310454155285.98酉阳县0.07474111.226750.07650698.3143.2349酉阳县21.0129.69131151066.41彭水县0.196326.6799780.03993592.499.40098彭水县16.1927.411289167483.42江津市0.14117110.35680.16094297.2291.4983江律市32.5435.911365284299.74合川市0.1385118.3979630.14026192.2141.8018合川市20.5130.310276277299.34永川市0.09653114.138340.08252892.1176.056永川市37.4339.511864284299.9南川市0.11298111.869060.1113279.3134.711南川市27.4935.89363235496.68南川市8.85102911.869060.1113279.3134.711南川市27.4935.89363235496.68社会发展水平综合评价指标人口素质部分I 正会发展水平综合评价指标(顼尊活质量部分)区县人口出生£每万人拥彳人均图书才在校中小巴每万人拥有专业技术人员数(人城镇居民，衣村居民，在岗职工3衣村居民，衣村改水2、 运用均值法对处理后的数据消除量纲3、 对指标实际值按比重法转换成评价值(消除量纲)，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ej6、 计算差异系数dj=1-ej7、 归一化处理，dj/dj之和实验结果如下：

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。二、综合指数评价法、功效系数法综合评价方法是指在综合评价中使用的综合汇总方法依据的数学原理相对于模型综合法而言较为简单的综合评价方法。1、综合指数评价法综合指数评价法：指用实际值与标准值进行对比后再使用线性综合汇总得到综合评价分值的方法。步骤及结果：1、 计算各指标值的的指标评价标准xi02、 计算个体指标数（个体指标数=指标的实际值与评价标准值之间的比值），部分结果显示如下：区县人口出生率（％,）每万人拥有执业医师助理人均图书拥有量（册）在校中小学生£每万人拥有专业技术人员数（人）重庆市0.912815281.0430778530.9963197561.0078356350.980886816万州区0.7856580331.208889490.4935284941.0314735710.950596938涪陵区渝中区大渡口［1.0843225731.2518529521.3661669230.9680809251.2297875961.7858690473.6361513317.936674511.023952413.8400847131.249053241.538160420.7146233721.0293246682.088380304江北区1.136859181.8736640830.7140477531.0561859591.91974849沙坪坝［次龙坡［南岸区1.2370006791.1685561760.8283038510.9992400221.4874060571.1308620421.5152143920.5491891771.0551115072.5438854591.2292331151.3811523540.2190847180.9863466021.823995879北/区1.4426087941.1682453724.950354241.0024633771.272562685万盛区1.0378298521.1219803640.7154849120.9960166670.902909391双桥区渝北区0.7015375910.907024220.2815686270.9960166671.9388226120.8159966160.723391540.7794722091.0132078930.89884162巴南区1.1617631061.0793826540.4625594580.9960166670.938266788黔江区0.642512480.7051755370.7781959961.0314735710.80682383长寿区某江县0.9855282930.9812049310.4922079071.057260410.8223604540.9897673390.9309851060.3363613651.0142823450.843504701潼南县0.9404444710.7087849430.4336054731.0411436360.55960746铜梁县大足县荣昌县1.3937258281.2713682090.4234932670.9960166670.8095814621.420723180.6606068930.4631624881.0314735710.6024319810.8460064971.0668022620.5301497870.9820487960.858806485璧山县1.2957437730.890382390.4692243751.0443669910.765276602梁平县1.0026423940.691608440.1080233460.9960166670.575971667城口县0.9271413210.9774338520.0710799640.7628606620.883401197丰都县0.6582044820.5607945450.2448712150.8874970520.567082236垫江县0.6362983950.7693509010.1744913270.9960166670.631895319武隆县0.827563220.8796531380.8185978531.0282502160.740574664忠县0.9965026650.8218767360.1568170350.9960166670.724139675开县0.6097734070.8698944430.6227041371.0626326690.492812687云阳县0.7564827720.772002880.1256473161.0121334420.65177327奉节县0.7668919920.485887170.3352060940.9970911190.532320653巫山县0.7097592250.5696008420.0394660231.0454414420.21864819巫溪县1.0162472940.6214320590.182909771.0132078930.620886037石柱县0.7191765340.8914179470.4539294570.964857570.498366347秀山县酉阳县0.4957183690.5878121560.2955141420.9530386020.6447216270.6539350790.8364555380.3048966241.0561859590.628977288彰水县1.7176747110.4976955240.1591507320.9927933120.436492365江律市1.2351511910.7716395320.6413977521.0443669911.280035328瓮川采用变异系数法求取各指标值饷权数，结果如下：吨978T010.9906444090.622684039永川市'* 0.844581564 1.'05338517 0.3288969550.9895699570.773102173南川市0.988512440.88431070.4436428930.8520401480.591546914/zrp |_1_ nr|epI—Ip||/|jLJ|-..I■r-r-.■■■..!■■. ss|/r-w1、人口素质0.361217人口出生率（唯）0.016768人均图书拥有量（册）0.029311在校中小学生体育锻炼达标率（%）0.158812每万人拥有专业技术人员数（人）0.003172人口素质0.0381492.生活质量0.078577城镇居民人均居住面积0.015712农村居民人均住房使用面积（平方0.007574在岗职工平均工资（元）0.010568农村居民人均纯收入（元）0.044933衣］寸改水累计受益率C%）0.008573、公益服务0.076376待染病发病率（1,10万）0.02183新生儿死亡率（％））0.025631电视人口覆盖率（%）0.002789每万人拥有公共文化设施面积（平70.050779城市基础设施投资占全社会固定资0.039727城镇居民人均公共绿弛面积（平方：＞0.043196城镇生活污水处理率仙）0.051248每万人拥有在校学生人数（人）0.009124、社会保护0.260931享受低保人数占救浇对象总人数的0.031856全社会保障支出占财政总支出的比0.018977每万人律师拥有人数（人）0.139435登记失业率（%）0.01428每万人治安案件发案率（件/万人）0.039726I-4J 士土— .■■■.TT.■■■.i-iOi-i区县人口素质综合评价值生活质量综合评价指标值公共服务部分指标社会保护指标社会结构指标值人均GDF（元）总指标值重庆市0.2447249740.0797870790.2362423670.227983720.0931836660.9043923930.282413万州区0.1665229380.0698591430.1656552540.2338612150.0911498880.7623793280.23361涪陵区0.3218258090.0796971230.2800796130.3331024610.0948798321.2059819780.374547渝中区3.1348346890.302168480.268687462.2852371570.293168812.8282177992.117763大渡口［0.2624559720.1052802860.3684178140.4609283770.1985901112.5047993510.550173江北区0.2639692690.1016194490.4356358850.6468403040.2075885911.7113076210.517382沙坪坝［0.246451960.0992787030.3110016920.3268878670.1979688451.7851995780.424971九龙坡［0.2509876750.1020664210.2125851930.261748050.1822377512.1589247740.441879南岸区0.1686014620.1043942380.280577870.3250404120.2013461161.6021633030.374592北珞区0.8963368350.089257080.3558810280.1910228830.1269398011.3586585680.571944万盛区0.2015216050.0785004040.197630910.1869810560.1326177660.8537092850.251804双桥区0.1601903840.0969532230.4402372750.3319962530.1349327512.1764882270.441123渝北区0.1961801860.1038676630.2778600080.2461682340.1081545171.0799014730.295738巴南区0.1635323130.0833219160.1211031090.1891705330.0976011461.1165338190.258371黔江区0.1890821280.0741712360.1568026450.1736946790.0582573080.7323960040.218782长寿区0.1581805880.0906919760.2000431140.2020394260.0748991091.1248137330.264816纂江县0.1326996270.0803991430.1564646050.1544223860.0985240620.7696556160.202407潼南县0.1300579070.0817747120.2025283130.1272912620.0547145880.7901044930.19543铜梁县0.1619356740.0976979410.2031128770.1747524980.0790081391.123935560.260193大足县0.1429960930.0829307490.2617774640.1416247110.0848526980.8612364790.219643荣昌县0.1655274930.0904928710.1439322040.1904880180.0711467750.7961262490.223419璧山县0.1548514550.0998798640.1575787220.1706036120.0983185411.1616969850.259547梁平县0.0793720580.0703114820.1107301080.0787519770.0612475430.614469960.137856城口县0.0916054870.0621883370.163955580.1321798310.0526921920.3891559440.133801丰都县0.0908120090.0783367860.2128682460.1175997910.0523950750.5736976580.155075垫江县0.0881973460.078498640.1452628060.1243067280.0528860470.640815140.158201武隆县0.2011778810.0715942990.2347727180.1315300330.0587460580.7410522770.218913忠县0.0964889780.0679143790.17223470.0649091160.0737367450.5340544340.137426开县0.156786720.0788140850.1793343040.0986762020.0588584590.566045010.171311云阳县0.0833427470.0643067410.2431370390.1404482680.0562778080.3838869080.139001奉节县0.1038066710.069295170.4142603980.1185834150.046257430.4364518150.158853巫山县0.0465221960.0706454280.1505395720.1050067950.0468694690.4311827790.114068巫溪县0.0912041180.0587508860.1540839580.104225480.044387910.307234980.115369石柱县0.1323502630.0645481430.1624625870.1313302210.049949750.4832458730.158463秀山县0.1000919110.0693738180.1408010880.1352204790.0496687830.4719550820.145272酉阳县0.1112495020.0594002220.1565768550.1091448640.0428321970.3155148940.124879彭水县0.0884662210.0623788550.0919004440.1797616580.0458626080.4372045350.144151江律市0.1973359820.0952639110.2009935090.1819251250.0958826891.1194192430.27586合jll币0.1543308360.0845733250.1207046050.147539180.0861193641.0556889980.236263永川市0.1299031920.099489630.1687139340.1941126470.099660461.0824105380.248876南川市0.1382214060.0819136770.130006970.1381368880.0626139761.0078913150.2206195、对总指标值做折线图如下:值标指总况状展发会社重庆市各区县社会发展状况分析值标指总况状展发会社重庆市各区县社会发展状况分析市*4•必罗」区^区,犯I县亥县县M土4县愚n市"俞中坪坝!碚渝北"铜梁璧山酒忠奉节石柱彭水永川沙区县分析：由图可以看出，除渝中区社会发展水平比较高外，其他各区县总体水平相近。5、对各项子指标做雷达图重庆市各区县社会发展水平「1重庆市重庆市各区县社会发展水平-■-万州区+涪陵区人口素质综合评价值人均GDP（元）生活质量综合评价指标值社会结构指标值公共服务部分指标社会保护指标—人口素质综合评价值人均GDP（元）生活质量综合评价指标值社会结构指标值公共服务部分指标社会保护指标— 大渡口区I-江北区沙坪坝区九龙坡区南岸区北碚区万盛区双桥区渝北区巴南区」黔江区长寿区■■—慕｝ 女ifA分析：渝中区的人口素质综合评价值、社会保护指标远远高于其他各区县，而南充市在人口素质、人均GDP、社会结构、社会保护、公共服务、生活质量上均处于劣势。重庆市区的发展明显的显示出一枝独秀，重点地区辐射作用。6、对GDP作折线图

重庆市各区县分析：渝中区、大渡口、双桥区、九龙坡区国民生产总值比较高。结论：重庆市整体社会发展水平比较均衡，作为重庆市的母城和中此乃城区，渝中区在人口素质、公益服务、社会保护、国民生产总值方面都占绝对优势。渝中区在社会结构和生活质量方面略微不足。具体可能是由于，渝中区作为重庆市的经济中心，注重发展第三产业，故在社会结构方面有所偏颇，而贫富差异的增大使得生活质量指标值变小。2、功效系数法功效系数评价法是指使用功效系数的计算公式惊醒消除量纲后再进行综合评价的方法。步骤：1、 用max(),min()分别计算出各指标值的满意值和不允许值2、 使用功效函数计算出各地区的功效系数，结果如下：3、 绘出各区县的功效系数折现图，结果如下：

I区县人口素质3生活质量3公共服务3社会保护捐土会结构4人均GDF（元） I总指标值重庆巾70.2821276.2266280.47252124.595468.1500769.4749937872.36907万州区72.4939971.6757178.05443138.117666.7612767.2216969470.86148涪陵区69.0414377.5944678.41136113.581667.8069174.2602637575.66564渝中区86.7544484.7708277.3922360.266682.80949100107.6797大渡口匚71.9468885.5407175.37706160.28276.0063894.8683752294.66082江北区73.7511880.4529683.03834205.963972.1358482.2781786586.43623沙坪坝［69.0214380.9102579.05163213.359275.9694883.450609687.49297丸龙坡匚74.2118883.2465679.12705114.577768.2093389.380442988.27925南岸区69.73581.9914180.2903191.624872.8333680.5464045884.29612北珞区69.5318177.8569481.4969147.206971.9119876.682756979.26639万盛区68.7579372.9476878.6709172.250775.2775768.6708136473.65284双样区74.2469283.747286.56847120.251872.3875689.6591191889.21537渝北区70.4424385.164381.38192139.401870.8590672.2597661175.69779巴南区67.7537575.3584674.78224153.922271.1285872.8410052375.99061黔江区73.442474.0337478.0839985.5565264.5947366.7459567168.4252