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1、RoughSets:AnIntroductionRoughSets:AnIntroductionIntroductionInformation/DecisionSystems(Tables)IndiscernibilitySetApproximationReductsandCoreRoughMembershipDependencyofAttributesIntroductionRoughsettheorywasdevelopedbyZdzislawPawlakintheearly1980’s.Repres
2、entativePublications:Z.Pawlak,“RoughSets”,InternationalJournalofComputerandInformationSciences,Vol.11,341-356(1982).Z.Pawlak,RoughSets-TheoreticalAspectofReasoningaboutData,KluwerAcademicPubilishers(1991).Introduction(2)Themaingoaloftheroughsetanalysisisi
3、nductionofapproximationsofconcepts.RoughsetsconstitutesasoundbasisforKDD.Itoffersmathematicaltoolstodiscoverpatternshiddenindata.Itcanbeusedforfeatureselection,featureextraction,datareduction,decisionrulegeneration,andpatternextraction,etc.Itcanidentifypa
4、rtialortotaldependenciesindata,eliminateredundantdata,giveapproachtonullvalues,missingdata,dynamicdataandothers.BenefitsEvaluationoftheimportanceoffeaturesReductionofredundantobjectsandfeaturesDeterminationofminimalsubsetsoffeaturesensuringsatisfactorycla
5、ssificationofobjectsCreationofmodelsforobjectsinvariousdecisionclassesResultsintheformclosetonaturallanguage(decisionrules)InformationSystems/TablesISisapair(U,A)Uisanon-emptyfinitesetofobjects.Aisanon-emptyfinitesetofattributessuchthatforeveryiscalledthe
6、valuesetofa.AgeLEMSx１16-3050x216-300x331-451-25x431-451-25x546-6026-49x616-3026-49x746-6026-49DecisionSystems/TablesDS:isthedecisionattribute(insteadofonewecanconsidermoredecisionattributes).TheelementsofAarecalledtheconditionattributes.AgeLEMSWalkx１16-30
7、50yesx216-300nox331-451-25nox431-451-25yesx546-6026-49nox616-3026-49yesx746-6026-49noIssuesintheDecisionTableThesameorindiscernibleobjectsmayberepresentedseveraltimes.Someoftheattributesmaybesuperfluous.IndiscernibilityTheequivalencerelationAbinaryrelatio
8、nwhichisreflexive(xRxforanyobjectx),symmetric(ifxRythenyRx),andtransitive(ifxRyandyRzthenxRz).TheequivalenceclassofanelementconsistsofallobjectssuchthatxRy.Indiscernibility(2)LetIS=(U,A)beaninformationsystem,thenwit
