论文A葡萄酒的评价

葡萄酒的评价摘要葡萄酒的质量主要从三个方面去评选，即理化指标，感官品评和卫生指标。这道题主要是让我们从酿酒葡萄与葡萄酒的理化指标入手，分析酿酒葡萄与葡萄酒的理化指标等之间存在的关系，并且分析品酒师的感官评分与酿酒葡萄，葡萄酒的理化指标之间是否存在某种关联，从而判断能否有理化指标来评出葡萄酒的优劣。第一问中品酒师靠的是感官品评，我们采用偏差度来判断哪一组的品评是更可靠。第二问根据酿酒葡萄的理化指标和葡萄酒的质量来给酿酒葡萄分等级，我们采用了权重归一方法先求出各酒样的最终评分，然后根据灰色关联度找出几个重要指标进行分析。再对葡萄酒进行分级，然后再将几个主要的理化指标进行分级，再根据同一等级的葡萄酒它们对应的酿酒葡萄的等级范围从而来判断酿酒葡萄的等级。第三问，根据所给的酿酒葡萄和葡萄酒的理化指标的数据，来判断葡萄酒和酿酒葡萄的理化指标的联系。实际上就是想通过这个问题的解决，从而用这两个理化指标来判断葡萄酒的好坏，这一问与第四问有一定的联系。而对于第四问，通过对酿酒葡萄和葡萄酒理化指标，再加上第一问的葡萄酒质量的总分进行对比，然后得出结论。关键字理化指标偏差度权重归一方法灰色关联度问题的提出确定葡萄酒质量时一般是通过聘请一批有资质的评酒员进行品评。每个评酒员在对葡萄酒进行品尝后对其分类指标打分，然后求和得到其总分，从而确定葡萄酒的质量。酿酒葡萄的好坏与所酿葡萄酒的质量有直接的关系，葡萄酒和酿酒葡萄检测的理化指标会在一定程度上反映葡萄酒和葡萄的质量。附件1给出了某一年份一些葡萄酒的评价结果，附件2和附件3分别给出了该年份这些葡萄酒的和酿酒葡萄的成分数据。请尝试建立数学模型讨论下列问题：1.分析附件1中两组评酒员的评价结果有无显著性差异，哪一组结果更可信？2.根据酿酒葡萄的理化指标和葡萄酒的质量对这些酿酒葡萄进行分级。3.分析酿酒葡萄与葡萄酒的理化指标之间的联系。4．分析酿酒葡萄和葡萄酒的理化指标对葡萄酒质量的影响，并论证能否用葡萄和葡萄酒的理化指标来评价葡萄酒的质量？问题的分析葡萄酒的质量品评的主要手段有理化指标，卫生指标和感官品评，本题的提出，主要是想问能否只用理化指标来判断葡萄酒的质量。问题一是感官品评，给出两组数据让我们选出较可信，即是同一组的品评师的品酒的偏差不能太大，不然对于该酒的品评就会失去公平性。问题二利用葡萄酒的质量和酿酒葡萄的理化指标来给酿酒葡萄分等级，附件中给出了酿酒葡萄的许多个理化指标，我们根据有关资料，选出对葡萄酒影响比较大的几个来分析。模型假设假设葡萄酒的卫生指标都一样；假设所有品酒师的水平都差不多；符号系统表示第一组第i号品酒师对第j种酒的打分结果；表示示第二组第i号品酒师对第j种酒的打分结果；表示第一组第i号品酒师对第j种酒的评分与第j种酒的总评分的比例；表示第二组第i号品酒师对第j种酒的评分与第j种酒的总评分的比例；表示第一组品酒师对第j种酒评分的偏差度；表示第二组品酒师对第j种酒评分的偏差度；表示第一组第j种酒的偏差在该组总偏差中所占的比重；表示第二组第j种酒的偏差在该组的总偏差中所占的比重；表示第一组中10位品酒师评分的总偏差度；表示第一组10位品酒师评分总偏差度的平均数；表示第二组10位品酒师评分的总偏差度；表示第二组10位品酒师评分总偏差度的平均数；，模型的建立和求解=1\*GB4㈠对于问题1的解答=1\*Arabic1．问题分析对比两种酒，四组数据，我们发现两组评选员的评选结果存在着很明显的差距。第一，第一组的评选员的评分标准相对于第二组评选员的评分标准要宽松许多；第二，在第一组中有一些评价较高的葡萄酒，在第二组的评价反而低了，而在第一组评价低的葡萄酒，在第二组的评价反而是高了。（这是根据同一号码的葡萄酒在不同组的排名情况来说的。）由于鉴定葡萄酒的主要手段是感官品评，而不同的品酒师有不同的习惯，爱好，品酒水平，因而不同的品酒师对同意种酒的评价不一样。由于题中所提到的是有资质的品酒师，我们假定这两组的品酒师水平相近，但是每一位品酒师对不同的酒产品进行评价时或多或少都会存在一定的偏差，造成对酒产品评价的不公平性，我们所做的就是计算两组品酒师中哪一组的偏差度较小，那么偏差度较小的那一组的数据就较可信。=2\*Arabic2．模型建立与求解令表示第一组第i号品酒师对第j种酒的打分结果，令表示第二组第i号品酒师对第j种酒的打分结果，（i=1,2……10；j=1,2……27）；第一组10位品酒师对第j种酒的总评分记为，第二组10位品酒师对第j种酒的总评分记为；第一组第i号品酒师对第j种酒的评分与第j种酒的总评分的比例记为（i=1,2……10，j=1,2，……27），第二组第i号品酒师对第j种酒的评分与第j种酒的总评分的比例记为，为第一组品酒师对第j种酒评分的偏差度（j=1,2……27），为第二组品酒师对第j种酒评分的偏差度，（j=1,2……27）表示第一组第j种酒的偏差在该组总偏差中所占的比重（i=1,2，……，10，j=1,2，……27）表示第二组第j种酒的偏差在该组的总偏差中所占的比重（i=1,2，……，10，j=1,2，……27）。第一组中10位品酒师评分的总偏差度为（i=1,2，……10），第一组10位品酒师评分总偏差度的平均数为，第二组10位品酒师评分的总偏差度为（i=1,2，……10），第二组10位品酒师评分总偏差度的平均数为。然后我们比较第一组和第二组的总偏差度的平均数大小，对比两组的偏差度，我们可以看出，出第二组品酒师的评分总偏差度比较小，所以我们认为第二组的评分比较可信。以下是我们根据以上模型，用Excel软件计算出来的结果：红葡萄酒第一组品酒师得分和总得分品酒师酒样品12345678910总分151664954776172617462627271818674918083798573803380858976698973838476804452646566588276638377686574747262846368848171733672697161826969648184722763707664598472598484715864766565767269857576723977787682859076928079815106782836875737568767574211736072636371706690737011254424055536047615869539136984795973777776757774614707770708059767676767301569505058515056606776587167280807169718074787474917707991689782698081767931863654955525762587068599197684846668878078828178620788476688279767686817862173909671696079738674771227383726893727577798077223838586809593819184788562470859068908470757870780256078816270676462816769226738071617871727679777382770776364807673678575730红葡萄酒第二组品酒师得分和总得分品酒师酒样品12345678910总分168718052537671737067681275767671687483737371740382698078637572777476746475797372607773736070712566687775767372727468721665677561586670676767663768656865477057747267653871707851626973596859660981838576698083777573782106773826263666672657268811646167625066645167646161267687558637367726971683137464686570677076696568814717178646776748073727261562607354597171706869657167165787064736675686969917727375747577797676687451867658055626462746065654197265826164817680747172620807580667084798371707582180727572627763707378722227779756268697371697371623797780836779807181747712466697273736872767670715256868846260666973666668226686783647374777863737202771647271697182737369715白葡萄酒第一组品酒师得分和总得分品酒师酒样品12345678910总分18580886176938380957982027847865479918568738174238567897578751367990798534757780657783887885867945844777607962747479747106614583657856806765846847848183667480806877827758754681548159737785837149796981607055738176857291075428660877583739171743117946856074718662887272312644275526762775668706331382428349666576626569659147848846779647868817372015744887718161796774827241669498665709187628477740178154907078718774929178818864483717271856474817311975668368736480637377722208068827183818462878077821844985597686837088847642265489058727776708074710237166806980827871877575924825679736759687886857332586808269746777787781771267566827593918176908481327584079675955667473776482866758969888785768890813白葡萄酒第二组品酒师得分和总得分品酒师酒样品12345678910总分1847882757984816975727792797677857779805976707583857471877979804583737564847874836982846677727695837979807787827384918156837574697577806777787557787974696982806172787428747874677377796673627239777889888489855479818041086777782818784617390798117983786360738161607671412738173796779804464847241368787981787275626581739147577767678827968788277115837788808483806376707841668637560678667715264673177769798379878875788880318758382797484787174677671976757870818083667877764208674757885817861737576621818079858376805885857922280768288758980667286794237480808074797573837677424678077777978836572837612579767986838883528584795268072758371838353628174327727984797683776379787702875828181788479717689796Pj、Qj如下表：红葡萄酒酒样品第一组品酒师第二组品酒师10.0461170.03986220.0235660.01632830.0252580.02228640.32270.02707450.0322290.01537660.0321140.02079670.0427090.03637180.0275270.03667890.0211280.019461100.0222920.026227110.0360010.030039120.0496750.022016130.0269570.01705140.0246580.019884150.0472750.029361160.017040.019242170.0354910.012192180.0344130.032522190.0262720.030689200.0194790.024737210.0419260.024761220.0276490.02064230.0199760.019364240.0332840.013739250.034850.02909260.0227380.02686270.0289950.018997白葡萄酒酒样品第一组品酒师第二组品酒师10.0351340.01959120.0573310.02772330.0672030.04736940.0252640.02531350.0475130.01886960.0559470.01894170.0242260.02625880.0569320.02314890.0396360.038465100.0588830.031543110.0552230.039375120.0509980.049036130.0594890.027762140.0445310.015505150.0475350.028131160.0540880.040423170.0457130.023168180.0513480.021506190.0283040.020039200.0309450.027706210.0516050.030398220.0497560.027662230.0261160.013201240.0431440.024475250.0226480.038943260.0315060.040958270.0556330.023232280.0330990.018986=2\*GB4㈡对问题2的解答=1\*Arabic1．问题分析根据葡萄酒的理化指标，通过搜集资料，我们选取了10个酿酒葡萄的理化指标，它们分别是：花色苷、酒石酸、柠檬酸、总酚、单宁、总糖、还原糖，出汁率、果皮质量、多酚氧化酶活力，再根据葡萄酒的分数，采用灰关联分析方法，选出酿酒葡萄的几个重要理化指标，然后根据葡萄酒的质量，分析我们所选的几个理化指标以此来分酿酒葡萄的等级。灰关联分析是依据灰数列间几何相似的序化分析与关联测度，来量化不同层次中多个序列相对某一级别的关联性，其实质为灰色系统中多个序列之间接近度的序列分析，这种接近度称为数据间的关联度。关联度愈高，说明该样本序列隶属的关系愈贴近，这是综合评价的信息和依据。在数学理论上，它反映了离散数列空间的接近度，所以是一种几何分析法。灰关联度分析的基本思想是根据离散数据之间几何相似程度来判断关联性大小，并进行排序。=2\*Arabic2．模型的建立和求解=1\*GB2⑴对附件中的数据进行变换处理，使其消除量纲和具有可比性。设为灰关联因子集，为参考序列，为比较序列，分别为与的第个点的数，由第一题可知，第二组数据更可信，因此在此我们选用第二组的红葡萄酒数据与白葡萄酒数据进行分析。首先，对于红葡萄酒的评分，我们根据第一题的数据，运用权重归一法，可以得到第二组红葡萄酒和白葡萄酒的最终得分，如下表1所示，通过对下表2进行变换处理得到红葡萄酒的x序列，如下表3，红葡萄酒第二组最终得分酒样品123456789最终得分68.96674.87274.87271.49171.51866.50070.42866.36078.348酒样品101112131415161718最终得分68.66962.35068.71668.72372.84266.15169.78074.34165.084酒样品192021222324252627最终得分72.99276.08172.97971.98977.42771.21167.95571.43371.453白葡萄酒第二组最终得分酒样品1234567最终得分78.77677.07677.47177.40681.42375.99474.937酒样品891011121314最终得分73.29182.32980.49072.45774.04474.93977.484酒样品15161718192021最终得分80.04666.93179.94277.51777.28477.66380.624酒样品22232425262728最终得分79.72677.75176.93580.99975.25978.08779.899表1红葡萄酒分数花色苷酒石酸柠檬酸总分单宁总糖还原糖出汁率果皮质量氧化酶酒样168.96621408.02782.0601.83023.60422.019208.175237.66878.4000.11033.753酒样274.87243224.36679.9300.77026.87523.361205.000229.13677.5000.16330.904酒样374.87243157.93938.0801.05021.68520.373256.190273.75871.8330.17019.303酒样471.4912279.68513.7700.55010.6988.638189.722237.76652.9670.17415.534酒样571.51757120.60619.4901.44017.61814.486209.663195.46065.6330.27031.536酒样666.4999546.18632.830010.67115.17299244.384223.81771.933330.19333336.773酒样770.4278460.76655.8200.5409.2145.619209.861303.95071.5000.14125.591酒样866.35962241.39695.7102.51015.24122.489198.849196.99059.5670.26050.434酒样978.34833240.843313.2301.10030.11424.362193.690194.92577.9670.13016.869酒样1068.6693644.20342.4500.2409.47616.688167.202161.42171.7000.20010.427酒样1162.349767.78739.2901.9006.0754.543209.563237.89158.4100.10214.260酒样1268.7162232.34266.0801.13012.0597.169247.659262.15563.3000.24321.080酒样1368.7230365.32384.3001.15014.3859.822197.857212.23768.1000.16028.076酒样1472.84154140.25685.7301.63014.65713.941191.508255.33566.1530.25541.577酒样1566.1511552.79196.2302.06011.90125.417179.107208.93367.6970.21325.743酒样1669.7796460.66019.0302.38011.21410.086204.008189.27571.8330.13513.648酒样1774.3413859.42365.8800.88015.33615.730212.738271.50471.5330.33017.174酒样1865.0841740.22763.600.5207.3815.388226.032265.77363.0670.16027.077酒样1972.99153115.70415.5600.13017.42613.700205.794220.33367.4330.16230.408酒样2076.0810323.52303.5100.44012.6778.115193.194227.33859.5330.23212.439酒样2172.9790689.281615.5102.38016.19213.613205.794259.11060.4000.10818.123酒样2271.9891274.026596.4900.77016.44212.155224.147226.39957.4330.14721.824酒样2377.42698172.62584.0800.39029.70424.257207.679212.56477.4670.23316.406酒样2471.211144.88078.3601.7008.75114.417201.825244.51276.7330.24715.066酒样2567.9554449.643352.8700.16011.5029.324150.337156.03858.5000.22014.280酒样2671.4331158.469197.1500.8207.3483.778173.353197.37768.3000.23032.026酒样2771.4526634.190336.2301.2608.89710.310196.667213.21659.5000.20023.035表2x0x1x2x3x4x5x6x7x8x9x101.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.08560.54994.82040.42081.13861.06100.98480.96410.98851.48480.91561.08560.38713.92230.57380.91870.92521.23071.15190.91621.54550.57191.03660.19531.83010.30050.45320.39230.91141.00040.67561.58180.46021.03700.29564.60680.78690.74640.65791.00710.82240.83722.45450.93430.96420.11321.37380.00000.45210.68911.17390.94170.91751.75761.08951.02120.14892.82520.29510.39040.25521.00811.27890.91201.28480.75820.96220.59162.77181.37160.64571.02130.95520.82880.75982.36361.49421.13600.59036.42230.60111.27581.10640.93040.82020.99451.18180.49980.99570.10831.18930.13110.40140.75790.80320.67920.91451.81820.30890.90410.01914.50971.03830.25740.20631.00671.00090.74500.92730.42250.99640.07932.95150.61750.51090.32561.18971.10300.80742.21210.62450.99650.16012.08740.62840.60940.44610.95040.89300.86861.45450.83181.05620.34372.78160.89070.62100.63310.91991.07430.84382.31821.23180.95920.12943.02431.12570.50421.15430.86040.87910.86351.93640.76271.01180.14874.38351.30050.47510.45810.98000.79640.91621.22730.40431.07790.14562.85440.48090.64970.71441.02191.14240.91243.00000.50880.94370.09861.74760.28420.31270.24471.08581.11830.80441.45450.80221.05840.28362.69900.07100.73820.62220.98860.92710.86011.47580.90091.10320.05771.70390.24040.53710.36850.92800.95650.75942.10610.36851.05820.21887.52911.30050.68600.61820.98861.09020.77040.98480.53691.04380.18143.15050.42080.69660.55201.07670.95260.73261.33640.64661.12270.42311.98060.21311.25841.10160.99760.89440.98812.12120.48611.03250.35514.05830.92900.37070.65470.96951.02880.97872.24240.44640.98530.12171.39320.08740.48730.42350.72220.65650.74622.00300.42311.03580.14333.47090.44810.31130.17160.83270.83050.87122.09090.94881.03610.08383.02430.68850.37690.46820.94470.89710.75891.81520.6825表3（2）定义为灰关联系数。其中为绝对差，为两极最小差，为两极最大差，为分辨系数（一般取0.5）。定义：设为指标的权重，满足，，定义为对的灰关联度，是序列几何距离的一种度量。通过excel进行计算可以得到r的值如下表4所示，r1r2r3r4r5r6r7r8r9r100.81030.65340.86710.88560.89040.96790.96060.95050.82940.8973表4由此可以得到，关联度最大的几项分别是：r6>r7>r8>r10>r5，因此可以得到影响葡萄酒质量的5个主要的酿酒葡萄的理化指标，分别是：总糖，还原糖，出汁率，多酚氧化酶活性，单宁。同理，我们可以得到第二组白葡萄酒的x序列，如下表5所示，最终得到的关联度如下表6所示，x0x1x2x3x4x5x6x7x8x9x101.00001.00001.00001.00001.00001.00001.00001.00001.00001.00001.00000.97840.49340.89743.04440.95380.75971.18701.18960.95480.79700.20020.98343.40651.95200.00001.30641.01451.03171.24391.02361.04830.24480.98262.48071.14571.91110.98351.06801.18191.13700.99580.51350.63401.03360.47341.523212.00001.18490.89091.15931.37020.95311.09250.27850.96471.01871.37750.73331.97541.52751.06521.17811.08060.84250.28880.95133.02450.70203.02221.92401.60440.92411.29620.94140.70300.33710.93043.49691.25666.02220.96220.56740.90141.04981.08460.83011.14391.04514.49881.70368.82221.08961.50431.19671.17960.88870.67680.62931.02181.03061.21520.48891.44822.30051.24541.30090.97501.05940.62080.91980.49691.19214.22221.47181.12370.95520.93140.98850.71630.75150.93990.49930.76824.82221.58971.08991.19611.34070.98730.94750.35980.95133.06280.81132.64442.20630.72230.87930.95131.06061.54420.51650.98360.49270.54801.08890.99760.81021.01251.35621.06400.65190.61981.01611.98950.91891.84441.66240.93330.97111.13840.97661.12570.16320.84965.00930.95203.62220.93830.75590.97511.15990.98381.01381.02611.01482.55021.69040.20001.23220.76231.09920.97701.03520.49720.40070.98400.99080.65891.31112.24071.96191.05101.06331.13920.61190.50110.98112.52981.55305.44440.88540.75241.13771.12450.95300.88400.59010.98591.01251.763210.71110.98401.06581.25561.25821.04290.93230.57311.02350.99981.40731.44440.81840.66241.19551.22220.95780.67400.46781.01212.01521.48513.93331.20112.19260.95521.20700.94470.50140.71000.98701.51861.37090.64440.96071.14971.13891.35680.94330.58980.39250.97660.45421.15231.06672.01552.88601.31001.21620.91721.23480.27491.02820.81811.15072.46671.43660.93531.27371.36631.02800.90750.67110.95542.02281.12750.20001.08981.87201.28451.39080.77060.64390.35620.99130.51301.374210.91113.17912.12081.08901.20390.88160.94890.3