模糊数学Ch6_Sec3-5

CH6FuzzySyntheticevaluation(p.198),产品质量评定科研成果签定环境评判火灾安全评估体操、跳水、舞蹈、歌唱等比赛.,6.3FuzzySyntheticEvaluationModels(p.202),Definition6.3.1Letamappingsatisfythefollowingconditions.,(1)Regularity(2)MonotonenondecreasingForalli(3)Continuityiscontinuoustoeachvariable.Thenfissaidan-aryfuzzysyntheticfunction.,Example6.3.1Thefollowingmappingsarealln-aryfuzzysyntheticfunctions.(1)(2)(3)isanunitaryweightvector(4)isanormalizingweightvector(5),Let(1)Unitaryweightvector(2)Normalizingweightvector,6.3.1Weightedaverage,Thenissaidaweightedaveragetypedfuzzysyntheticevaluation.,Letbeaunitaryweightvectorand,6.3.2Geometricaverage,Letbeaunitaryweightvectorand,6.3.3Singlefactordecision,Letbeanormalizingweightvectorand,Thenissaidasinglefactordecisiontypedfuzzysyntheticevaluation.,6.3.4Principlefactorprominence,Letbeanormalizingweightvectorand,Fuzzysyntheticevaluationisconcludedasthefollowingsteps.Step1ConstituteaattributesetofevaluationobjectionsStep2ConstituteevaluationsetStep3Constituteone-factorevaluation,i.e.afuzzymappingfromUtoF(V)F(V),Fuzzyrelationisinducedby,i.e.Thismatrixiscalledevaluationmatrixofsinglefactorandorderedtriplet(U,V,R)isnamedevaluationspace.Step4Synthesizebychoosingappropriatefuzzysyntheticfunction.,Example6.3.3CostumeevaluationLetU=designandcolor,pattern,quality,price,comfortV=verywelcome,welcome,littlewelcome,nowelcomeForonesortofcostumewemayobtainone-factorevaluationbysomespecialists.Ifweonlyconsiderdesignandcolorthendesignandcolor,Verywelcomeby20%specialists,Example6.3.3CostumeevaluationFortheotherfactorswehaveThusevaluationmatrixis,Example6.3.3CostumeevaluationForgivenmaleclientswesupposetheirweightisSofuzzysyntheticevaluationisobtainedforthecostume.AndbynormalizingIfconsiderfemaleandweightisThentheirevaluationis,Example教师的教学质量评估问题U=教材熟练程度,逻辑性程度,启发性程度,生动有趣程度,板书整洁程度V=优秀,良好,一般,不好专家通过听课打分,对某教师授课的各因素进行评价得单因素评价矩阵权重为,U=教材熟练程度,逻辑性程度,启发性程度,生动有趣程度,板书整洁程度V=优秀,良好,一般,不好,Example人才选拔U=技术水平,科研水平,工作能力,经济支持,社会影响V=很好,较好,一般,不好某个人才经过评定得到单因素模糊关系矩阵R取A=(0.35,0.35,0.10,0.10,0.10)那么该人才的综合评价为:,那么该人才的综合评价为:归一化,上述人才我们称为甲,另有一人才乙,现对其进行同样的模糊评价,其单因素模糊关系矩阵R2那么乙人才的综合评价为:归一化,为了计算方便,将评语集数量化为(很好、较好、一般、不好)S=(0.4,0.3,0.2,0.1)所以:经过最后评定乙的优先度略要高于甲,所以最后选择乙.,Example对某工人考核记录如下表,表中w1表示平时多次考核,w2表示晋级考核.,有10次经常性考核,从因素u1考核,有5次被评为v1,6.5MultilevelSyntheticEvaluationModels(p.218)ProblemWhentomanyfactorsareusedtherearethefollowingproblemsintheprocessofevaluation.Itishardtodistributeweightsrightly.one-factorevaluationinformationarelostbyoperationsandsincetheweightsaresmallwidely.,Example6.5.1ProductionevaluationFactorsset:U=u1,u2,u9Evaluationset:V=v1,v2,v3,v4v1Firstclass,v2Secondclass,v3Inferior,v4Waster.,次品,Example6.5.1ProductionevaluationOne-factorsevaluationmatrixisAndletFuzzysyntheticevaluationis,MultilevelSyntheticEvaluationStep1FactorClassificationFactorssetU=u1,u2,unisdividedassclasses,i.e.AndTheysatisfythefollowingconditions.(1)(2)(3)Step2EvaluationSet,Step3WeightSet(1)FactorsclassweightsetIftheweightoffactorsclassUiisai(i=1,2,s)thenfactorsclassweightsetis(2)FactorsweightsetTheweightaijofjthfactoruijinithfactorsclassUiis,Step4ThefirstlevelsyntheticevaluationConsiderfuzzysyntheticevaluationforeachfactorineveryclass.Letone-factorevaluationmatrixofthefirstlevelsyntheticevaluationisThefuzzysyntheticevaluationforithfactorsclassis,Step5ThesecondlevelsyntheticevaluationTheone-factorevaluationmatrixofthesecondfuzzysyntheticevaluationisfirstlevelsyntheticevaluationmatrixFinallythesecondlevelfuzzysyntheticevaluationis,Example6.5.1considere.g.6.5.2againFactorssetUisdividedasthreeclassesfactorssetTheirone-factorevaluationmatrixesare,Example6.5.1considere.g.6.5.2againThesecondone-factorevaluationmatrixisAndlettheweightvectorofU1,U2andU3isThesecondsyntheticevaluationis,Example某化工厂在使用某种剧毒液体氰化钠时不慎将其流入河里,河中的鱼蚌大批死亡,危害了下游人们的生命安全,由此受到起诉.法院受理了这一案件,并用模糊综合评判方法研究其中的犯罪事实.考虑犯罪因素集U=污染程度U1,污染范围U2,危害程度U3对于U1,其因素集与评语集分别为U1=生物需氧量,化学需氧量,氨氮,溶解氧V1=严重,中等,轻度,清洁,归一化,对于U2,其因素集与评语集分别为U2=分子量,溶解度,颗粒吸着量,水流量V2=很远,远,较远,近对于U3,其因素集与评语集分别为U3=人身危害,社会经济损失,厂家经济损失V3=很严重,严重,较严重,一般,归一化,二级综合评价:,Example模糊决策方法定量评价道路安全性,Example模糊决策方法定量评价道路安全性路上发生不安全事件可能性为评价集:很大(V1),较大(V2),一般(V3),小(V4),路上导致不安全事件因素发生可能性评价,Example模糊决策方法定量评价道路安全性,(0.2,0.2,0.4,0.2)(0.2,0.2,0.4,0.2)(0,0.4,0.6,0)(0,0.2,0.2,0.6)(0,0,0.2,0.8)(0.2,0.2,0.6,0)(0.4,0.2,0.4,0)(0.8,0,0.2,0)(0.6,0,0.2,0.2)(0.4,0.2,0.4,0)(0.2,0.4,0.4,0)(0,0.2,0.8,0),R1R2R3R4,Example模糊决策方法定量评价道路安全性使用M(+,.)得一级综合评价B1=A1R1=(0.1091,0.2909,0.4909,0.1091)B2=A2R2=(0.10,0.15,0.40,0.35)B3=A3R3=(0.5818,0.0545,0.2545,0.1091)B4=A4R4=(0.34,0.22,0.44,0)由此得到二级综合评价,Example模糊决策方法定量评价道路安全性归一化25.99%的人评判为发生不安全事件可能性很大,27.75%的人评判为发生不安全事件可能性较大,34.80%的人评判发生不安全事件可能性一般,还有11.45%的人评判发生不安全事件可能性较小。,Example企业素质的模糊综合评判模型,企业素质,职工队伍素质装备工艺素质管理组织素质,领导班子素质中层干部素质一般管理人员素质工程技术人员素质工人素质技术装备素质生产工艺素质管理基础工作素质管理组织体制素质专业与综合管理素质管理装备素质,CH7FuzzyRelationalEquation(p.198),PositiveproblemInputAOutputB=?