不协调目标信息系统的知识约简

26120031CHINESEJOURNALOFCOMPUTERSVol.26No.1Jan.20031)1),2)1),3)1)(710049)2)(050016)3)(316004):2002203224;:2002209208.(2001AA113182).,,1940,,,.E2mail:[e-mail].,,1966,,,.,,1964,,,.,.,.,;,.;;;TP18KnowledgeReductionsinInconsistentInformationSystemsZHANGWen2Xiu1)MIJu2Sheng1),2)WUWei2Zhi1),3)1)(InstituteforInformationandSystemSciences,FacultyofScience,XianJiaotongUniversity,Xian710049)2)(CollegeofMathematicsandInformationScience,HebeiNormalUniversity,Shijiazhuang050016)3)(InformationCollege,ZhejiangOceanUniversity,Zhoushan316004)AbstractKnowledgereductionisoneofthemostimportantproblemsinroughsettheory.Therearemanytypesofknowledgereductionsintheareaofroughsets.Itisrequiredtoprovidetheirconsistentclassification.Butmostofinformationsystemsarenotconsistentbecauseofvariousfactorssuchasnoiseindata,compactrepresentation,predictioncapabilityandsoon.Toacquirebriefdecisionrulesfrominconsistentsystems,knowledgereductionsareneeded.Themainobjectiveofthispaperistoin2troduceanewconceptofknowledgereductionininconsistentsystems.Itisreferredtoasmaximumdistributionreduction,whichpreservesallmaximumdecisionrules.Themaximumdistributionreduc2tioneliminatestheharshrequirementsofthedistributionreductionandovercomesthedrawbackofthepossiblereductionthatthederiveddecisionrulesmaybeinincompatiblewiththeonesderivedfromtheoriginalsystem.Therelationshipsamongdistributionreduction,maximumdistributionreduction,ap2proximatereductionandassignmentreductionareexamined.Thejudgementtheoremsanddiscernibili2tymatrixeswithrespecttothosereductionsareobtained,fromwhichwecanprovidenewapproachestoknowledgereductionsininconsistentinformationsystems.Keywordsroughset;inconsistentsystem;knowledgereduction;consistentset1[1].[14],.,.,,.,,.,,,,.,,[49].,.,.,.,[10],,.,.[10],.,;,.,4,..2...1.(U,A,F,D,G),U,U=x1,x2,,xn;A,A=a1,a2,,ap;D,D=d1,d2,,dq;FUA,F={fk:UVk,kFp},Vkak;GUD,G={gk:UVk,kFq},Vkdk.BAA,RB=x,y:fk(x)=fk(y),PakB;RD=x,y:gk(x)=gk(y),PdkD.RBRDU,BD.UU/RB=[x]B:xU,U/RD=[x]D:xU.[x]B=y:x,yRB,[x]D=y:x,yRD.xBD.PXAU,RB(X)=xU:[x]BAX=[x]B:[x]BAX;RB(X)=xU:[x]BXÁ=[x]B:[x]BXÁ.RB(X)RB(X)XB.XBX,BX.RB(X)AXARB(X),RB(X)ARB{a}(X),RB(X)BRB{a}(X).:X.2.(U,A,F,D,G),RAARD,,.,.3(U,A,F,D,G),U/RD=D1,D2,,Dr;B(x)=DD1/[x]B,D2/[x]B,,DDr/[x]B,xU.DDj/[x]B=Dj[x]B[x]B.311:,B(x)U/RD.mB(x)=maxjFrDDj/[x]B=DDji/[x]B,xU.mB(x).y[x]B,yDjiB(x)=Dji:DDji/[x]B=maxjFrDDj/[x]B,xU.3.(U,A,F,D,G),BAA.(1)PxU,B(x)=A(x),B.B,B,B.(2)PxU,B(x)=A(x),B.B,B,B.,.B(U,A,F,D,G),BA.B(U,A,F,D,G),BA,.1.(U,A,F,D,G),..B,.1.,.(1).1Ua1a2dx1111x2111x3121x4121x5122x6222{a1},.B(x)=Dj:[x]BDjÁ,xU;B=1Urj=1RB(Dj).2.B:(1)RB(Dj)={[x]B:B(x)={Dj}}.(2)RB(Dj)={[x]B:DjB(x)}.(3)BAA,B(x)BA(x),xU..(1)[x]BADjZDj[x]BÁ,Pkj,[x]BDk=ÁZDjB(x),Pkj,Dk|B(x)ZB(x)={Dj}.(2)DjB(x)ZDj[x]BÁ.(3)BAA]RBBRA]PxU,[x]BB[x]A..3.B:(1)1FBFr;(2)B=1ZRB(Dj)=Dj,PjFr;B=rZRB(Dj)=U,PjFr;(3)BAA]RB(Dj)BRA(Dj)]BEA,PjFr..RB(Dj).BB.4.(U,A,F,D,G).(1)PxU,B(x)=A(x),B.B,B,B.(2)B=A,B.B,B,B.,.4.(U,A,F,D,G),..B,PxU,B(x)=A(x),DDj/[x]B=DDj/[x]A,PjFr.DjB(x),Dj[x]BÁ,DDj/[x]B0,DDj/[x]A0,Dj[x]AÁ,DjA(x).A(x)BB(x).2(3)A(x)=B(x),PxU.B.2.,,(2).{a1},.2Ua1a2dx1111x2112x3122x4121x5122x62224120031..:1{a1},.2{a1},.5.(U,A,F,D,G),BAAZB..:BZB.B,PxU,B(x)=A(x).,PjFr,xRB(Dj)Z[x]BDjÁZDjB(x)ZDjA(x)Z[x]ADjÁZxRA(Dj).RB(Dj)=RA(Dj),B=A,B.,B,B=A,rj=1|RB(Dj)|=rj=1RA(Dj).PjFr,RB(Dj)BRA(Dj),RB(Dj)=RA(Dj).,PxU,DjB(x)Z[x]BDjÁZxRB(Dj)ZxRA(Dj)Z[x]ADjÁZDjA(x).PxU,B(x)=A(x),B.4:]TZ4.6().(U,A,F,D,G),BAA.(1)BPx,yU,A(x)A(y),[x]B[y]B=Á.(2)BPx,yU,A(x)A(y),[x]B[y]B=Á.(3)BPx,yU,A(x)A(y),[x]B[y]B=Á..J([x]B)=[y]A:[y]AA[x]B.BAA,J([x]B)[x]B.(1)B(U,A,F,D,G).Px,yU,[x]B[y]BÁ,[x]B=[y]B.B(x)=B(y).A(x)=B(x),A(y)=B(y),A(x)=A(y).A(x)A(y),[x]B[y]B=Á.,PxU,[y]AA[x]B,[x]B[y]BÁ,A(x)=A(y).kFr,DDk/[x]A=DDk/[y]A.[x]B={[y]A:[y]AJ[x]B},DDk/[x]B=[y]ADk:[y]AJ[x]B[x]B=[y]ADk[y]A[y]A[x]B:[y]AJ[x]B=DDk/[y]A[y]A[x]B:[y]AJ[x]B=DDk/[x]A[y]A[x]B:[y]AJ[x]B=DDk/[x]A.A(x)=B(x).B.(2)B.Px,yU,[x]B[y]BÁ,[x]B=[y]B.B(x)=B(y).A(x)=B(x),A(y)=B(y),A(x)=A(y).A(x)A(y),[x]B[y]B=Á.,PxU,[y]AA[x]B,[x]B[y]BÁ,A(x)=A(y).PDj0A(x),Dj0A(y).[x]B={[y]A:[y]AJ([x]B)},kFr,DDk/[x]B=[y]ADk:[y]AJ[x]B[x]B=[y]ADk[y]A[y]A[x]B:[y]AJ[x]BF[y]ADj0[y]A[y]A[x]B:[y]AJ[x]B=Dj0[x]B[x]B=DDj0/[x]B.Dj0B(x),A(x)AB(x).,PDj0B(x),Dj0|A(x),P[y]AJ[x]B,A(x)=A(y)mA(y)DDj0/[y]A.Dk0A(x),Dk0A(y),DDk0/[x]B=[y]ADk0[y]A[y]A[x]B:[y]AJ[x]B=mA(y)[y]A[x]B:[y]AJ[x]B511:DDj0/[y]A[y]A[x]B:[y]AJ[x]B=[y]ADj0[y]A[y]A[x]B:[y]AJ[x]B=Dj0[x]B[x]B=DDj0/[x]B.Dj0B(x).Dj0A(x),B(x)AA(x).B(x)=A(x),PxU.B.(3)B,Px,yU,[x]B[y]BÁ,[x]B=[y]B.B(x)=B(y).A(x)=B(x),A(y)=B(y),A(x)=A(y).A(x)A(y),[x]B[y]B=Á.,PxU,Dj0B(x),[x]BDj0Á.[x]B=[y]A:[y]AJ[x]B,[y0]AJ[x]B,[y0]ADj0Á,Dj0A(y0).[y0]AA[x]B,[y0]B[x]BÁ.A(x)=A(y0),Dj0A(x),B(x)AA(x).2(3)B(x)=A(x).B..6...5.(U,A,F,D,G),U/RA=C1,C2,,Cm.D31=[x]A,[y]A:A(x)A(y);D32=[x]A,[y]A:A(x)A(y);D33=[x]A,[y]A:A(x)A(y).fk(Ci)akCi.Dl(Ci,Cj)=akA:fk(Ci)fk(Cj),Ci,CjD3lA,Ci,Cj|D3l(l=1,2,3).l=1,2,3,Dl(Ci,Cj)CiCj.Dl=(Dl(Ci,Cj);i,jFm)(l=1,2,3).7.Dl(l=1,2,3):(1)Dl(l=1,2,3),Dl(Ci,Cj)=Dl(Cj,Ci),Pi,jFm;(2)A,Dl(Ci,Ci)=A,PiFm;(3)Dl(Ci,Cj)ADl(Ci,Cs)Dl(Cs,Cj),Pi,s,jFm..(3).ak|Dl(Ci,Cs)Dl(Cs,Cj),ak|Dl(Ci,Cs)ak|Dl(Cs,Cj).fk(Ci)=fk(Cs),fk(Cs)=f