信息系统中的知识与知识粒度

Knowledge,KnowledgeGranulationinInformationSystemJiyeLiangYuhuaQianKeyLaboratoryofComputationalSchoolofComputer&InformationTechnologyIntelligenceandChineseInformationProcessingofMinistryofEducationShanxiUniversityTaiyuan,PRC030006Taiyuan,[e-mail]@126.comAbstractGranularcomputingispotentiallyusedinknowledgediscoveryanddataminingetc.Basedoninformationsystem,theextentofclosenessanddifferencebetweenknowledgeismeasuredbyintroducingtheconceptsofknowledgeclosenessandknowledgedistance,theaxiomdefinitionofknowledgegranulationisgiven,andseveralknowledgegranulationsareallspecialformunderthedefinition.Theseresultswillbeveryhelpfulforunderstandingtheessenceofthegranulation,andhaveimportantinstructivesignificanceforestablishinggranularcomputingininformationsystem.Keywords:informationsystem,knowledge,knowledgedistance,knowledgegranulation.1IntroductionGranulationisoriginallyaphysicsconcept,usedtodenote“averagemeasureofgranules”.Physicsgranulationisfinepartitionofphysicsobjects,averagemeasureoftheirfinepartitioncanbedefinedasinformationgranulationcorrespondinglyforknowledgeandinformation.Asarecentlyrenewedresearchtopic,granularcomputing(GrC)isanumbrellatermtocoveranytheories,methodologies,techniques,andtoolsthatmakeuseofgranulesinproblemsolving1,2,3.BasicideasofGrChaveappearedinrelatedfields,suchasintervalanalysis,roughsettheory,clusteranalysis,machinelearning,databases,andmanyother2,4.L.A.Zadeh2proposedageneralmodelbasedonfuzzysetstheory,anddefinedandconstructedinformationgranulebyusingconceptofgeneralrestriction.Therelationshipbetweengranuleswasexpressedbyfuzzychartorfuzzyif-thenrules.Z.Pawlak5pointedthatallelementsinagranuleisaintegerbutnotindividuals.Informationlosingmeansthatsomesubsetsofuniversecanbeapproximatelydescribed.Roughsetstheorymainlyprocessapproximateproblemofinformationgranule.Y.Y.Yao6proposedthreekindsofgranularcomputingmodelsuchaspoweralgebra,intervalnumberalgebraandintervalsetalgebrabasedonsettheory.Besides,healsostudiedmanyaspectsofgranularcomputinginequivalence,tolerance),(AUS=,where:Uisafinitenon-emptysetofobjects；Aisafinitenon-emptysetofattributes；foreveryAa∈,thereisamappinga,a:aVU→,whereaViscalledthevaluesetofa.Foraninformationsystem),(AUS=,ifAa∈∀,everyelementinaVisadefinitevalue,thenSiscalledacompleteinformationsystem.LetAP⊆,wedefineequivalencerelation:)}()(,|),{()(vauaPaUUvuPIND=∈∀×∈=.Itiseasilyshownthat})({)(aINDPINDPa∈=I.)(/PINDUconstitutesapartitionofU.)(/PINDUiscalledaknowledgeinU,every(equivalenceclasses)inP.Let),(AUS=beacompleteinformationsystem,AQP⊆,,},,,{)(/21mPPPPINDUL=,},,,{)(/21nQQQQINDUL=.Wedefinepasfollows:QPp,ifandonlyif,forevery∈iP)(/PINDU,)(/QINDUQj∈∃suchthatjiQP⊆,andforsome)(/0PINDUPi∈,)(/0QINDUQj∈∃suchthat00jiQP⊂.Example1.ConsiderdescriptionsofseveralcarsasTable1.Table1.CarPriceSizeEngineMax-Speedu1lowcompactgasolinelowu2lowfulldieselhighu3highfulldieselmediumu4highcompactdieselmediumu5lowfullgasolinehighTable1isacompleteinformationsystem,where},,,,{54321uuuuuU=,and},,,{4321aaaaA=,where1a-Price,2a-Size,3a-Engine,4a-Max-Speed.ForAP⊆,},{21aaP=,itiseasilycomputedthat}}{},{},,{},{{)(/43521uuuuuPINDU=.2.2IncompleteInformationSystemForaninformationsystem),(AUS=,ifaVcontainsnullvalueforatleastoneattributeAa∈,thenSiscalledanincompleteinformationsystem.Furtheron,wewilldenotenullvalueby*11,13-15.LetAP⊆,wedefinetolerancerelation11,13-15:)()(,|),{()(vauaPaUUvuPSIM=∈∀×∈=or*