模糊数学中关于隶属函数的确定方法

1TheWaysofDeterminationtheMembershipFunction学院：理学院专业：应用数学姓名：张启亮学号：20145642ThewaysofdeterminationthemembershipfunctionzhangqiliangTosolvetheproblem,themembershipfunctionofasetofFshouldbefoundedfirstly,andthewaytofindF,whichbasedonpatternrecognitions,hasalreadymentionedabove.ThispartwetalkaboutfuzzyandthegeneralwaytofindF,andsomestationshouldbepaidmoreattention.StatisticsLetustakethewayofdeterminingyoungforexampletoexplainit.LetUisthefieldofage,AisF.Takeu=27,theFstatisticwaytodeterminetheofu.exway:pickseveralpersonsandletthemsettheirvalueofyoungafterthinkingtwice.Thismakethemeanofconceptoffuzzymoreprecise.Ifmisthecountoftheoccurrencethatageisinfieldof27,whilenisthetotalexperiment.m/nisthedegreeofmembershipfunction.Chart2-1istheresultofthesamplingsurvey.Wefindthefrequencydegreeofmembershipisaroundthe0.78,sowetakeA(27)=0.78.Chart2-1Wetakethememberfunctionofyoungintoconsideration.Let'smakethefieldofUintoserialgroups,andthemid-valueofeachgroupstandsforthefrequencydegreeofmembership(chart2-2).Plottheyoungcurveofthemembership(figure2-7).TheresultcomesfromonedepartmentinthestaticFway.Inthesameway,we'vegotthesimilarconsequencefromanthertwodepartments.TestNumber(n)102030405060708090100110120129MembershipNumber(m)61423313947536268768595101MembershipFrequency(m/n)0.60.70.770.780.780.760.760.780.760.760.750.790.783Chart2-2Figure2-7TheFexperimentshowstheregularofmembership.Themainfactorsoftheyoungis:jointhecorps(14),jointhearmy(18),overtheagecorps(25),retirefromcorps(28),specialages(20,25,30,35),matureandageandsoon,thesepointisshowedonthechart.Fstatisticsissimilartothestaticoneinform,andbothtoresearchthechancinessindefiningway.But,therearetwodifferencesbetweenFstatisticsandtheprobabilityandstatistics.Thesedifferencesare:GroupFrequencyMembershipFrequencyGroupFrequencyMembershipFrequency13.5-14.520.01625.5-26.51030.79814.5-15.5270.21026.5-27.51010.78315.5-16.5510.39527.5-28.6990.76716.5-17.5670.51928.5-29.5800.62017.5-18.51240.96129.5-30.5770.59718.5-19.51250.96930.5-31.5270.20919.5-20.5129131.5-32.5270.20920.5-21.5129132.5-33.5260.20221.5-22.5129133.5-34.5260.20222.5-23.5129134.5-35.5260.20223.5-24.5129135.5-36.510.00824.5-25.51280.9924Themainrequirementofrandomexperimentforthechanceevent:everytime,thebechancing(notbechancing)ofAiscertainty.EverytimeAiscertainty.wisrandom.Inexperiment,ThefrequencyoftheoccurrenceofA=(winA)/nThefrequencyismorestable,whenngetslarger.ThevalueofthefrequencystandsiscalledthePossibilityofAinsomeStatus.ThemainrequirementofFstatisticexperiment:thefixeduisbelongtoanassembleA,whoseelementsareunfixed,doajudgment.Thismeanseverytime,AisAfixassemble.Everyexperiment,uisfixed.Aisfluctuated.ntimes'experiment,calculateThedegreeoffrequencymembershipofu=(uinA)/nWhenngrows,thefrequencyismorestable.ThevalueofthisfrequencydefinedasthedegreeofutoA.TheFexperimentshouldfollowtherule:themenshouldlearnthemeaningoffuzzyvocabularyandtheabilitytofigureitoutinnumber;afteranalysisdroptheillegaldata.StaticF,alsocalledTwo-phasestaticF,whichmeansP2={A,A2}Ineveryevent,definedamape:U---P2It'sacompartmentalizationtoU.Two-phasestaticFmeansthereareonlytwoelementsintheassemble.Sothereisproperty:u∈U,A(u)+Ac(u)=1Basedonit,moretheoriesaboutthestaticFcanbegiven.SetP={A1,A2,A3.......Am}Ai∈A(U)i=1,2,3...meveryresultcangavemape:u-pWesaytheexperimentism-phasestaticFexperiment,thePism-aphaseassemble.Ex,{short,mid,tall}is3-aphase,{old,mid,young}is3-aphase,{east,north,south,west}is4-aphase,{gold,wood,water,fire,earth}is5-aphase,andsoon.Theresultofm-aphasecanleadtothefunctionofmembership,anditsproperity:5u∈U,A1(u)+A2(u)+A3(u)+...Am(u)=1TrichotomyTrichotomyisalsothemethodthatdealswithfuzzinessusingtheideaofrandominterval.Forinstance,wecanestablishthemembershipfunctionofthreeconceptssuchastheset1Aofshorty,theset2Aofmediumandtheset3Aofhigh.Incaseof)3,0(U,mistheunit,3P={shorty,medium,high},wecanidentifyapartitionofUaftereachtestandeachdivisiondeterminatesacoupleofnumbers(,)::thecut-offpointofshortyandmedium:thecut-offpointofmediumandhighOtherwise,ifweknowthecoupleofnumbers(,),wecanconfirmamape,inotherwordswecanseparatetheshorty,mediumandhigh.Sofuzzyconceptsareclear.Theregionsofshorty,mediumandhigharerandom,sothatandarerandom.Theyhavethecharacteristicsofnormaldistribution::),(211aN,:),(222aNAndthecoupleofnumbers(,)confirmsthemap),(e:U{1A,2A,3A}PromptlyFigure2-86xxAxxAxxAxe)()()())(,(321P{x}indicatestheprobabilitythatintheregionbx,.Ifxincreases,thenbx,willbereduced,andtheprobabilitythatintheregionbx,isreduced.ThecharacterofP{x}issimilartothefuzzyset)(1xA:xdxxPxPxA)(}{)(1Sameargument:xdxxPxPxA)(}{)(3)(xPand)(xParetheprobabilitydensityofand,andbecause)()(1)(312xAxAxAWecancalculate:223111)(,1)(axxAaxxAAndthen22112)(axaxxAInthatxtdtex2221)(.SelectionoffunctionandparameteradjustmentDuetothefuzzysetisfuzzyandtheempiricalstudyobject,correctlydeterminethemembershipfunction,isthebasisofusingthefuzzysettheorytosolvepracticalpr