模糊数学ch6sec课件

1、模糊数学ch6secCH6 Fuzzy Synthetic evaluation (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.模糊数学ch6sec6.3 Fuzzy Synthetic Evaluation Models (p.202)12nxxxx12(,)nf x xxx(1)(2)iixx(1)(2)111111( ,)( ,)iiiniiinf xxxxxf xxxxx12(,)nf x xx:0,10,1nfDefinition 6.3.1 Let a mapping satisfy the following conditions.(1

2、) Regularity(2) Monotone nondecreasing For all i(3) Continuity is continuous to each variable. Then f is said a n-ary fuzzy synthetic function.模糊数学ch6secExample 6.3.1 The following mappings are all n-ary fuzzy synthetic functions.(1)(2) (3) is an unitary weight vector(4) is a normalizing weight vect

3、or(5)1121( ,)nniif x xxx2121( ,)nniifx xxx13121(,)() ,nppniiifx xxa x0,p 12(,)na aa4121( ,),nniiifx xxa x12(,)na aa15121( ,)()nnniifx xxx模糊数学ch6secLet (1) Unitary weight vector(2) Normalizing weight vector12( ,)0,1nnAa aa11niia11niia模糊数学ch6sec6.3.1 Weighted average 121(,)nniiifx xxa x12( ,)0,1nnx xx

4、fThen is said a weighted average typed fuzzy synthetic evaluation.12(,)0,1nnAa aaLet be a unitary weight vector and模糊数学ch6sec6.3.2 Geometric average 12( ,)0,1nnx xx121( ,)inaniifx xxx12( ,)0,1nnAa aa Let be a unitary weight vector andfThen is said a geometric average typed fuzzy synthetic evaluation

5、. 模糊数学ch6sec6.3.3 Single factor decision 12( ,)0,1nnx xx121( ,)nniiifx xxax 12( ,)0,1nnAa aaLet be a normalizing weight vector andfThen is said a single factor decision typed fuzzy synthetic evaluation. 模糊数学ch6sec6.3.4 Principle factor prominence 12( ,)0,1nnx xx121( ,)nTniiifx xxaTx 12(,)0,1nnAa aaL

6、et be a normalizing weight vector andTfThen is said a principle factor prominence typed fuzzy synthetic evaluation. Where T() is t-norm. 模糊数学ch6secFuzzy synthetic evaluation is concluded as the following steps.Step 1 Constitute a attribute set of evaluation objectionsStep 2 Constitute evaluation set

7、 Step 3 Constitute one-factor evaluation, i.e. a fuzzy mapping from U to F (V) F (V) 12 ,nUu uu12 ,mVv vv:U1212( )iiimiimrrruuvvv01,1,1ijrinjm 模糊数学ch6sec Fuzzy relation is induced by , i.e.This matrix is called evaluation matrix of single factor and ordered triplet (U, V, R) is named evaluation spac

8、e. Step 4 Synthesize by choosing appropriate fuzzy synthetic function.111212122212mmnnnmrrrrrrRrrr模糊数学ch6secExample 6.3.3 Costume evaluation Let U=design and color, pattern, quality, price, comfort V=very welcome, welcome, little welcome, no welcomeFor one sort of costume we may obtain one-factor ev

9、aluation by some specialists. If we only consider design and color then design and color1(0.2,0.5,0.3,0)R Very welcome by 20% specialists模糊数学ch6secExample 6.3.3 Costume evaluation For the other factors we have Thus evaluation matrix is2(0.1,0.3,0.5,0.1)R 3(0,0.1,0.6,0.3)R 4(0,0.4,0.5,0.1)R 5(0.5,0.3

10、,0.2,0)R 0.20.50.300.10.30.50.100.10.60.300.40.50.10.50.30.20R模糊数学ch6secExample 6.3.3 Costume evaluation For given male clients we suppose their weight is So fuzzy synthetic evaluation is obtained for the costume.And by normalizingIf consider female and weight is Then their evaluation is (0.10,0.10,

11、0.15,0.30,0.35)A(0.35,0.3,0.3,0.15)BA R0.35 0.3 0.3 0.15(,)(0.32,0.27,0.27,0.14)1.1 1.1 1.1 1.1(0.3,0.35,0.10,0.10,0.05)A(0.21,0.315,0.37,0.105)模糊数学ch6secExample 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0.450.250.200.100.500.400.1000.300.4

12、00.200.100.400.400.100.100.300.500.100.10R(0.30,0.20,0.20,0.20,0.10)A模糊数学ch6sec 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0.450.250.200.100.500.400.1000.300.400.200.100.400.400.100.100.300.500.100.10R(0.30,0.20,0.20,0.20,0.10)A( , ):M (0.30,0.25,0.20,0.10)BA R( , ):M (0.135,0.080,0.060,

13、0.030)BA R( , ):M (0.405,0.365,0.150,0.08)BAR 模糊数学ch6secExample 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:0.350.390.220.040.170.350.390.090.000.300.440.260.090.220.300.390.430.350.220.00R模糊数学ch6sec那么该人才的综合评价为:归一化 BA R(0.30,0.30,0.30

14、,0.1)B 0.350.390.220.040.170.350.390.09(0.35,0.35,0.10,0.10,0.10)0.000.300.440.260.090.220.300.390.430.350.220.00(0.35,0.35,0.35,0.1)模糊数学ch6sec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 22BA R2(0.35,0.41,0.12,0.12)B 0.300.600.100.000.300.600.100.00(0.35,0.35,0.10,0.10,0.10)0.400.30

15、0.200.100.100.200.600.100.200.200.300.30(0.30,0.35,0.10,0.10)20.300.600.100.000.300.600.100.000.400.300.200.100.100.200.600.100.200.200.300.30R模糊数学ch6sec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优先度略要高于甲, 所以最后选择乙.220.40.3(0.35,0.41,0.12,0.12)0.300.20.1TNB S110.40.3(0.30

16、,0.30,0.30,0.1)0.280.20.1TNB S模糊数学ch6secExample 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. WUVv1v2v3v4w1u1u2u3u40.50.500.60.30.10.70.1 00.20.300.20.200.3w2u1u2u3u40000000010000111有有10次经常性考核次经常性考核, 从因素从因素u1考核考核,有有5次被评为次被评为v1模糊数学ch6sec(0.35,0.35,0.15,0.15)A 0.300.180.400.120.300.060.120.5200.420.180.400.360

17、.0600.58R(0.30,0.18,0.35,0.35)A R WUVv1v2v3v4w1(0.6)u1u2u3u40.50.500.60.30.10.70.1 00.20.300.20.200.3w2(0.4)u1u2u3u40000000010000111模糊数学ch6sec6.5 Multilevel Synthetic Evaluation Models (p.218)ProblemWhen to many factors are used there are the following problems in the process of evaluation. It is ha

18、rd to distribute weights rightly. one-factor evaluation information are lost by operations and since the weights are small widely. 模糊数学ch6secExample 6.5.1 Production evaluation Factors set: U=u1, u2, ,u9 Evaluation set: V=v1, v2, v3, v4 v1 First class, v2 Second class, v3 Inferior, v4 Waster.次品模糊数学c

19、h6secExample 6.5.1 Production evaluation One-factors evaluation matrix is And letFuzzy synthetic evaluation is 0.360.240.130.270.200.320.250.230.400.220.260.120.300.280.240.180.260.360.120.200.220.420.160.100.380.240.080.200.340.250.300.110.240.280.380.18R(0.10,0.12,0.07,0.07,0.16,0.10,0.10,0.10,0.1

20、8)W (0.18,0.18,0.18,0.18)BWR0.100.100.120.120.070.070.070.070.160.160.100.100.100.100.100.100.180.18模糊数学ch6secMultilevel Synthetic EvaluationStep 1 Factor ClassificationFactors set U=u1, u2, , un is divided as s classes, i.e.And They satisfy the following conditions.(1) (2)(3)Step 2 Evaluation Set 1

21、2,iiiiinUuuu1,2,is12snnnn12sUUUU(, )()iji j ijUU12 ,pVv vv模糊数学ch6secStep 3 Weight Set(1) Factors class weight setIf the weight of factors class Ui is ai (i=1,2,s) then factors class weight set is (2) Factors weight setThe weight aij of jth factor uij in ith factors class Ui is 1,2,is12(,)sAa aa12(,)

22、iiiiinAaaa1,2,is模糊数学ch6secStep 4 The first level synthetic evaluationConsider fuzzy synthetic evaluation for each factor in every class. Let one-factor evaluation matrix of the first level synthetic evaluation isThe fuzzy synthetic evaluation for ith factors class is ( )( )( )11121( )( )( )21222( )(

23、 )( )12iiiiiipiiipiiiinnn prrrrrrRrrriiTiBAR( )( )( )11121( )( )( )2122212( )( )( )12(,)iiiiiiipiiipiiinTiiinnn prrrrrraaarrr12(,)iiipb bb模糊数学ch6secStep 5 The second level synthetic evaluationThe one-factor evaluation matrix of the second fuzzy synthetic evaluation is first level synthetic evaluatio

24、n matrix Finally the second level fuzzy synthetic evaluation is 111222TTssTsBARBARRBAR112212( ,)TTTTpsTsARARBARAb bbAR模糊数学ch6secR1R2Rs.A1A2As RBAB1B2Bs模糊数学ch6secExample 6.5.1 consider e.g. 6.5.2 againFactors set U is divided as three classes factors set Their one-factor evaluation matrixes are 1123

25、,Uu u u2456,Uu u u3789,Uu u u10.360.240.130.270.200.320.250.230.400.220.260.12R20.300.280.240.180.260.360.120.200.220.420.160.10R30.380.240.080.200.240.250.300.110.240.280.300.18R1(0.30,0.42,0.28)A 2(0.20,0.50,0.30)A 3(0.30,0.30,0.40)A 111(0.30,0.32,0.26,0.27)BAR222(0.26,0.26,0.20,0.20)BAR333(0.30,0

26、.28,0.30,0.20)BAR模糊数学ch6secExample 6.5.1 consider e.g. 6.5.2 againThe second one-factor evaluation matrix isAnd let the weight vector of U1, U2 and U3 isThe second synthetic evaluation is 1230.300.320.260.270.260.260.200.200.300.280.300.20BRBB(0.20,0.35,0.45)A(0.30,0.35,0.30,0.20)BA R模糊数学ch6sec Exam

27、ple 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1(0.20,0.57,0.21,0.02)A 10.810.19000.790.200.0100.880.090.03000.010.490.5R11(0.57,0.20,0.03,0.02)AR 归一化1(0.70,0.24,0.

28、04,0.02)B 模糊数学ch6sec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2(0.6,0.1,0.1,0.2)A 20.10.70.200.20.60.10.100.20.20.600.40.50.1R222(0.1,0.6,0.2,0.1)BAR归一化3(0.46,0.36,0.09,0.09)B 3(0.1,0.6,0.3)A 300.10.20.70.50.40.100.40.50.10R33

29、(0.5,0.4,0.1,0.1)AR 模糊数学ch6sec二级综合评价:(0.5,0.3,0.2)A(0.5,0.3,0.2,0.1)BA R1230.70.240.040.020.100.600.200.100.460.360.090.09BRBB 模糊数学ch6secExample 模糊决策方法定量评价道路安全性道路安全人的因素U1 (0.275)行人过错U11 疲劳驾驶U12驾驶员不遵守交通规则U13车的因素U2 (0.2)车辆维修保养不完善U21车辆设计不合理U22车辆装载超标U23路的因素U3 (0.275)道路几何参数U31路面条件U32安全设施U33环境因素U4 (0.25)人

30、车管理U41地理位置U42气候环境U43模糊数学ch6secExample 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(V 1 ) ,较大(V 2 ) ,一般(V 3 ) ,小(V 4 ) 路上导致路上导致不安全事不安全事件因素发件因素发生可能性生可能性评价评价模糊数学ch6secExample 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模糊数学ch6secExample 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 =A1 R1= (0. 1091, 0. 2909 ,0. 4909 ,0. 1091)B2 =A2 R2 = (0. 10 ,0. 15 ,0. 40 ,0. 35)B3 =