XML模糊查询.docx

XML模糊查询.docx

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XML模糊查询

FuzzyXQuery

MarleneGoncalves

UniversidadSimónBolívar,Caracas,Venezuela

mgoncalves@usb.ve

LeonidTineo

UniversidadSimónBolívar,Caracas,Venezuela

leonid@usb.ve

Abstract  WepresenthereafuzzysetbasedextensiontoXQuerythatallowusertoexpresspreferencesinqueryingXMLdocumentsobtainingdiscriminatedanswers.Theextensioncomprisesthenewxs:

truthbuilt-indatatypeintendedtorepresentgradualtruthdegreesaswellasthexml:

truthattributeforhandingsatisfactiondegreesinnodesproceedingsoffuzzyXQueryexpressions.Thelanguageisextendedtodeclarefuzzytermsandusetheminqueryingexpressions.Alsoanevaluationmechanismispresentedinordertoavoidsuperfluouscalculationsoftruthdegrees.

Introduction

TheWebplaysanessentialroleinmanyonlinecompaniesandithasmadeavailableanexorbitantamountofdatafromseveralwebsites.Manywebsitesofferonlineservicesforbookingflights,hotels,railpasses,cruises,etc.Thus,theWebhasbeenbecomeanindispensabletoolforthiskindofwebsites.

Supposeresearcherswhowanttoattendaconferenceandtherefore,theydecidetoquerythebestflightforthemusingatravelcompanywebsite.Aflightmaybeselectedforaresearcherifandonlyifistheveryeconomicalandmakesfewstops.However,asecondresearcherprefersaflightwhosedestinationisanearcityandthenhemaytakeatraintoarrivecitywherewillbeheldtheconference.Thus,researchesmaydefineseveralcriteriatotakeafinaldecision.Sincemanyflightsmaybereturnedbywebsites,itisnecessarytodiscriminatequeryanswersandsortthembyuser-criteria.Apossiblesolutionisfuzzydatabasemanagementsystemswhichallowdefininguser-criteriaandrankingqueryanswersbyamembershipfunction;amembershipfunctionquantifiesthesatisfactiongradeofeachanswerwithrespecttouser-criteriaandinducesatotalorderofthesetobjects.

Additionally,atravelwebsitemayhaveincompletedataonflights,e.g.,lackofinformationaboutsometaxes.Inconsequence,severalonlinetravelcompaniesmaysharedataandcommunicateamongthemselvesinordertorespondaresearch’squery.Usually,mostofthesewebsitesmayuseXML（ExtensibleMarkupLanguage）format[6]tointerchangedata.XMLisaformatrecommendedbytheWorldWideWebConsortium（W3C）andithasbeenextensivelyusedtotransferdataamongwebsites.XMLdatamaybequeriedthroughdeclarativequeryinglanguagessuchasXPath[10]andXQuery[12].BothlanguagesareXML-centric,i.e.,theirdatamodelandtypesystemarebasedonXML.

XQueryisanextensionofXPathandistheW3CstandardlanguageforXMLdata.Mostofdatabaseengines（IBM,Oracle,andMicrosoft）supportXQueryanditisanativeXMLquerylanguageconceivedtointegratemultipleXMLsources.

Ontheotherhand,XMLstructuremaybedefinedusingDocumentTypeDefinition（DTD）[6]andXMLSchema[11].XMLSchemaistheW3CsuccessorofDTDanditisthetypesystemofXQuery.Furthermore,XMLSchemaismoreextensiblethanDTDandiseasiertoshareuser-definedextensionwithnamespacesupport.

Inourqueryexample,aresearcher’squerymayretrieveeitherapossiblylargesubsetofXMLdatafromseveralwebsitesthatbeuselessfortheresearcheroremptyanswersbecauseofdatabaseenginesofthewebsitesarebasedonBooleanlogic.Thus,theresearcherhastodiscardirrelevantanswerswhensizeofqueryresultishuge,interestinganswersmaybelostifqueryresultisemptyandthereisnotdiscriminationonqueryresultintermsofalluser-criteria.Fuzzy-logic-basedlanguageshavebeensuccessfullyemployedtoexpressuser-criteriaanddiscriminatequeryanswers.Severalfuzzyquerylanguagesforrelationaldatabasehavebeenintroduced:

SQLf[3],FSQL[7,8]andSoftSQL[2].Inthispaper,weproposetoincorporatefuzzylogictoXQuerylanguageasasteptowardsprovidingamoreflexiblenativeXMLlanguage.WesupposeXQuerysyntaxisfamiliarforreader.DetailsofXQueryaregiven[12].WeextendatmostallXQueryvalidexpressionsinordertoallowfuzzyconditions.

Background

In[13],Zadehintroducedfuzzysetsasanextensionofclassicalones.Afuzzysetisasetwhoseelementspossessmembershipdegreesdeterminedbyamembershipfunction.AmembershipfunctionofafuzzysetF,denotedbyF,isafunctionintorange[0,1]thatinducesatotallyorderedset.

Fuzzysetsarethebasisoffuzzylogic.Fuzzylogic isamulti-valued logicwhosetruthvaluesarerepresentedbyrealnumbersontheclosedinterval[0,1]wherecompletelyfalsecorrespondstoazerovalueandcompletelytrueisindicatedbyonevalue.Thetruthvalueofapropositionsisdenotedby（s）.

Linguistictermsmaybespecifiedusingfuzzylogicandtheyexpressuser’scriteria.Thesetermsmayhelpustoidentifyfuzzytermssuchaspredicates,modifiers,connectives,quantifiersandcomparators.Afuzzypredicateisthebasicterminfuzzylogicanditisexpressedinnaturallanguagebypositiveadjectives,suchasgood,bad,cheap,andexpensive.Afuzzymodifiertransformsamembershipfunctionofafuzzypredicatebyincrease,decrease,translateoreverse.Inmostcases,adverbsveryandextremelyindicatefuzzymodifierpresence,e.g.,verycheapandextremelyexpensivemodifymembershipfunctionsofpredicatescheapandexpensive.Afuzzyconnectiveisanoperatortoconnectfuzzyconditionsbynegation,conjunctionand/ordisjunction.Afuzzycomparatorisapredicatedefinedonpairsofelements.ComparativeadjectivesexpressedinEnglishbyterminationerorthewordmoreandpureadjectivessuchasbetterandworse,areexamplesoflinguistictermsrepresentedasfuzzycomparators.Finally,fuzzyquantifiersareextensionofuniversalandexistentialones.Quantitativeadjectivesasfewandmany,andrelativesuperlativeasmostofareinstancesoffuzzyquantifiers.Theymaybeabsoluteorproportional[REF].Absolutequantifiersaredefinedonrealnumbersandtheydescribefuzzyquantitiessuchasabout5ormorethan20.Proportionalonescorrespondtonumbersintoclosedinterval[0,1]andtheydefinerelativequantitiessuchasatleasthalformostofhalf.

Someimportantconceptsoffuzzysetstheoryaresupport,core,and-cut.Theyallowstabilizingrelationshipsbetweenfuzzysetsandclassical.Supportoperatorallowsdefiningthoseelementsthatarenotfullyexcludedfromthefuzzyset,i.e.,asetofelementswhosemembershipdegreeisgreaterthanzero.Coreoperatorallowsidentifythoseelementsthatarefullyincludedintheset,thisis,asetofelementswhosemembershipdegreeis1.Finally,-cutoperatordefinesasetofelementswhosemembershipdegreeisgreaterorequalthan[0,1].

Sincemembershipfunctioncalculationandfuzzysetscontainmoreelementsthanclassicalones,timecomplexityoffuzzyqueriesevaluationmaybehigherthancrispqueryevaluation.Forthisreason,Boscetal.[REF]haveconceivedanevaluationmechanismbasedin-cutdistributionoverconditionsinvolvedinaafuzzyqueryinordertotranslateafuzzyquerytoaregularone.ThismechanismisknownasDerivationPrinciple.MorerecentlyMa[REF]hasproposedtheuseofthisprincipleasanunifiedapproachforfuzzyqueryevaluationonrelationaldatabases.ThisprinciplehasbeenwidelystudiedbyTineoetal.[REF],showingbenefitsofitsapplication.

Thederivedqueryselectsthedesiredsubsetofdatawithoutcomputingthesatisfactiondegreeoffuzzyconditionforthecompleteinputdata.Ifsizeofdatasubsetisexactlyequaltosizeof-cut,derivationissaidtobeastrongderivation.Ifthissubsetisasupersetof-cut,thenderivationissaidtobeweak[REF].

Toillustratethisprinciple,wedenoteDS（）astheregularsentencederivedfromafuzzysentenceusingqualitativecalibrationandDNC（,,）asderivednecessaryconditionthatspecify-cutofafuzzycondition.

Fig.1.Representationofthefuzzypredicateeconomical

TheuserrequirementFindeconomicalflightswithathresholdof0.5maybespecifiedinSQLf[3]as:

select*fromflightswhereprice=economicalwithcalibration0.5;

Wherewithcalibrationisaclauseforspecificationofthethreshold.LetassumethedefinitionoffuzzypredicateeconomicalasinFig.1.ApplyingtheDerivationPrinciple,weobtainaclassicSQLquerythatretrievesthesamerowsthatthefuzzyone.

DS（select*fromflightswhereprice=economicalwithcalibration0.5）=select*fromflightswhereprice1400

Thisqueryderivationobeysthefactthat,accordingtothedefinitionofthe-cutofafuzzset,wemayderivetheBooleancondition:

DNC（price=economical,,0.5）=price1400.

ThefuzzyqueryprocessingismadeontheresultofthederivedBoolenaquery,inthiscasesuperfluousaccessandcalculusforrowswithprice>1400wouldbeavoided.ThisstrategyhasreportedtoreducethequeryprocessingtimeforSQLf.

RelatedWorks

FSQL[7,8]andSQLf[3]aretwofuzzyextensionsofSQL.FSQLallowsprocessinginexactinformationandmostoffuzzytermsarepredefinedordefinedduringdatabasemodeling.SQLfsupportsfuzzytermdefinitionsandSQL:

2003[5]features.Bothlanguagesarerelationaldatabase-centric.

Analogously,XMLquerylanguageshavebeenextendedwithfuzzylogic.SomeideastoextendXPathwithfuzzytermswereintroducedin[4]:

rankedliststhroughannotations（orcomments）intheresult,anduseoffuzzypredicatesandfuzzyquantifiers.Nevertheless,theydonotallowusertodefinefuzzytermsbuttheyofferasetoffewbuilt-inpredicates;modifiers,comparatorsandconnectivesarenotconsideredin[4].Combinationoffuzzypredicatesismadebymeansofarithmeticoperationsonrankingvariablesinsteadof