(英文PPT4)模糊控制讲义第二章(2.5 2.6).ppt 26页

CHAPTER2FuzzyMathematics2.5FuzzyMatrix2.6FuzzyRelation 2.5FuzzyMatrix2.5.1Basicdefinitionsoffuzzymatrix2.5.2Supportoffuzzymatrix2.5.3Compositionoffuzzymatrix2.5.4Transposeoffuzzymatrix 2.5.1BasicdefinitionsoffuzzymatrixIf(,),thereexist,thenisafuzzymatrix.Usually,meansallthefuzzymatrixes(rows,lines).1Union:2Intersection: 2.5.1Basicdefinitionsoffuzzymatrix3Complement:4Contain:5Equal: 2.5.1BasicdefinitionsoffuzzymatrixExample2.5.1:Notes:Afuzzymatrixanditscomplementarenotcomplementaryeventssimilarwithfuzzysets.Example2.5.2: 2.5.1BasicdefinitionsoffuzzymatrixExample2.5.3: 2.5.2SupportoffuzzymatrixDefinition:iscalledthesupportmatrixof.Notes:ThesupportmatrixisaBooleanmatrix. 2.5.2SupportoffuzzymatrixExample2.5.4: 2.5.3CompositionoffuzzymatrixDefinition:,,,,thecompositionmatrixofthesetwomatrixesisafuzzymatrixwithrowsandlines,writtenaswhoseelementisThecompositionoffuzzymatrixisalsocalledasmultiplicationoffuzzymatrix. 2.5.3CompositionoffuzzymatrixExample2.5.5:Notes:(popularly) 2.5.4TransposeoffuzzymatrixRowschangeintolinesandlineschangeintorows. 2.6FuzzyRelation2.6.1Definitionoffuzzyrelation2.6.2Operationoffuzzyrelation2.6.3Compositionoffuzzyrelation 2.6.1DefinitionoffuzzyrelationRelation:AsubsetofaCartesianproductofand,iscalledadualisticrelationfromto(orrelationforshort).Fuzzyrelation:andaretwosets,isafuzzysubsetin,isalsocalledafuzzyrelationfromto.Thedegreeofmembershipofis 2.6.1DefinitionoffuzzyrelationFuzzyrelationcandescribedbyfuzzymatrixwhenandarefiniteset.When,itiscalledthefuzzyrelationin.Anelementinfuzzymatrixmeanstherelationbetweentheelementinandtheelementin. 2.6.1Definitionoffuzzyrelationisthespaceofheightinanareaandisthespaceofweight.,(cm),,(kg),therelationbetweenheightandweightisintable.Example2.5.6 2.6.1Definitionoffuzzyrelation405060708014010.80.20.101500.810.80.20.11600.20.810.80.21700.10.20.810.818000.10.20.81Fuzzyrelationbetweenheightandweight 2.6.1DefinitionoffuzzyrelationWecanfindfromtheaboveexamplethathowdoesfuzzymathematicsdescribethefuzzyconceptioninrealworldintheformofmath.Usingthismethod,wecanhandlethefuzzyconceptionincomputer. 2.6.2Operationoffuzzyrelationandaretwofuzzyrelationsin.1Union:2Intersection:3Contain:4Equal:5Complement:6Transpose: 2.6.2OperationoffuzzyrelationCharacteristicsoffuzzyrelation:1自反性2对称性Everyelementindiagonaloffuzzymatrixis1.3传递性 2.6.2OperationoffuzzyrelationExample2.6.1Twopeoplehavethefuzzyrelations:“similitude”“enemy”“love”“younger”自反性（Y）对称性（Y）传递性（N）自反性（N）对称性（Y）传递性（N）自反性（Y）对称性（?）传递性（?）自反性（N）对称性（N）传递性（Y） 2.6.2OperationoffuzzyrelationExample2.6.2自反性（Y）对称性（Y）传递性（N） 2.6.3Compositionoffuzzyrelationisaspaceofpeople,isthebrotherrelation,isthepaternity,istherelationbetweenuncleandnephew.,,arethreepeoplein,isabrotherof,isthefatherof,soshouldbetheuncleof.Wecalltherelationbetweenuncleandnephewisthecompositionbetweenthebrotherrelationandpaternity.Andwrittenas：Ifthen 2.6.3CompositionoffuzzyrelationInageneralway,，，isthespace,isacommonrelationfromto,isacommonrelationfromto,isacommonrelationformto,ifiscalledacompositionfromto,writtenas. 2.6.3CompositionoffuzzyrelationDefinition:Let，，bethespace,isafuzzyrelationfromto,isafuzzyrelationfromto,isafuzzyrelationformto,isthecompositionfromtowhohasthemembershipfunction:When，，isfinite,thecompositionoffuzzyrelationcouldbeexpressedbythecompositionoffuzzymatrix. Emphases1Operationoffuzzymatrix.2Characteristicsoffuzzyrelation. Words1模糊矩阵2模糊矩阵的合成3模糊关系fuzzymatrixcompositionoffuzzymatrixfuzzyrelation