Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Applications PDF
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ATLANTIS COMPUTATIONAL INTELLIGENCE SYSTEMS VOLUME 1 SERIES EDITOR: DA RUAN AtlantisComputational Intelligence Systems Series Editor: DaRuan, BelgianNuclear Research Centre(SCK•CEN) Mol&Ghent University,Gent,Belgium (ISSN:1875-7650) Aimsandscopeoftheseries Theseries‘AtlantisComputationalIntelligenceSystems’aimsatcoveringstate-of-the-art researchanddevelopmentinallfieldswherecomputationalintelligence(CI)isinvestigated andapplied. The seriesseeks to publishmonographsandeditedvolumeson foundations and new developments in the field of computational intelligence, including fundamental and applied research as well as work describing new, emerging technologies originating fromcomputationalintelligenceresearch.AppliedCIresearchmayrangefromCIapplica- tionsintheindustrytoresearchprojectsinthelifesciences,includingresearchinbiology, physics,chemistryandtheneurosciences. Allbooksinthisseriesareco-publishedwithWorldScientific. Formoreinformationonthisseriesandourotherbookseries,pleasevisitourwebsiteat: www.atlantis-press.com/publications/books AMSTERDAM –PARIS (cid:2)c ATLANTISPRESS/WORLDSCIENTIFIC Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Applications Zheng Pei XihuaUniversity,Chengdu, China Da Ruan Belgian NuclearResearch Centre (SCK•CEN), Mol & GhentUniversity,Gent, Belgium Jun Liu UniversityofUlster,Belfast, NorthernIreland, UK Yang Xu SouthwestJiaotongUniversity,Chengdu, China AMSTERDAM –PARIS AtlantisPress 29,avenueLaumie`re 75019Paris,France ForinformationonallAtlantisPresspublications,visitourwebsiteat: www.atlantis-press.com Copyright This book, or any parts thereof, may not be reproducedfor commercial purposes in any formorbyanymeans,electronicormechanical,includingphotocopying,recordingorany informationstorageandretrievalsystemknownortobeinvented,withoutpriorpermission fromthePublisher. AtlantisComputationalIntelligenceSystems ISBN:978-90-78677-11-6 e-ISBN:978-94-91216-28-2 ISSN:1875-7650 (cid:2)c 2009ATLANTISPRESS/WORLDSCIENTIFIC Preface Humansemploymostlynaturallanguagesindescribingandrepresentingproblems,com- putingandreasoning,arrivingatfinalconclusionsdescribedsimilarlyaswordsinanatural languageorastheformofmentalperceptions.Tomakemachinesimitatehumans’mental activities,thekeypointintermsofmachineintelligenceistoprocessuncertaininformation bymeansofnaturallanguageswithvagueandimpreciseconcepts. Zadeh(1996a)proposedaconceptofComputingwithWords(CWW)tomodelandcom- pute with linguistic descriptions that are propositions drawn from a natural language. CWW,followedtheconceptoflinguisticvariables(Zadeh,1975a,b)andfuzzysets(Zadeh, 1965),hasbeendevelopedintensivelyandopenedseveralnewvastresearchfieldsaswell asappliedinvariousareas,particularlyintheareaofartificialintelligence. Zadeh(1997,2005)emphasizedthatthecoreconceptionsinCWWarelinguisticvariables andfuzzylogic(orapproximatereasoning). Inalinguisticvariable,eachlinguisticvalue isexplainedbyafuzzyset(alsocalledsemanticsofthelinguisticvalue),itsmembership functionis defined on the universeof discourse of the linguistic variable. By fuzzy sets, linguisticinformationorstatementsarequantifiedbymembershipfunctions,andinforma- tion propagationis performedby approximatereasoning. The use of linguistic variables implies processes of CWW such as their fusion, aggregation, and comparison. Different computationalapproachesintheliteratureaddressedthoseprocesses(Wang,2001;Zadeh andKacprzyk,1999a,b).Membershipfunctionsaregenerallyatthecoreofmanyfuzzy-set theoriesbasedCWW. Apartfromfuzzy-settheoriesbasedCWW,thereexistsomealternativemethodsdeveloped to modelandcomputewithlinguisticinformationin naturallanguagesfromthedifferent point of view. This book provides a systematic introduction course of those alternative methodsto modify and overcomelimitations of CWW in the sense of Zadeh, e.g., diffi- v vi LinguisticValuesBasedIntelligentInformationProcessing cultyindeterminingandinterpretingfuzzysetmembershipfunctionsoflinguisticvalues, computationalcomplexityandlossofinformationduetolinguisticapproximations. Both ofthesestepsusuallyimplytheinvestigationofhumanfactor,semanticsofthelinguistic terms, and subjective beliefs. In this book, we introduce the so-called linguistic-valued based intelligent information process approach– some popular approachesin which the useofmembershipfunctionsassociatedtothelinguistictermsisunnecessaryorthemem- bership functiondoes notplay an importantor key role. The linguistic value reflects the useof“words”ascomputationalvariables,i.e.,thedirectuseoflinguisticvaluesinnatu- ral language, where the symbolic approachacts by the directcomputationand reasoning on linguistic terms. Although some work introduced in this book also cover the use of membershipfunctiontoinvestigatethesemanticsoflinguisticvariablesindifferentalter- nativeways, however,akeyinsightandthemainfocusbehindandwithinthisbookisto directlyrepresentandmanipulatetheavailablelinguisticinformationandknowledgefrom theordinalpointof view,the algebraicpointofviewor fromthe symboliclogicpointof view. Takingawiderperspectivethesetheories,methodsandalgorithmswillbenefitresearchers in a very wide variety of domains but in particular: AI and decision science, and espe- cially,insocialscienceandpoliticalscienceofteninvolvedinhumanjudgement,reasoning anddecisionmakingwithlinguisticevaluationinnaturallanguage. Thelinguisticformal methodinthisresearchdirectionnaturallylendstoan effectivemeansofcommunication betweenscholarsandpractitioners,sincetheapproachgreatlyfacilitatestheexchangeand analysisof“raw”linguisticinformation.Carryingoutsucharesearchwillprobablynotbe aneasytask,butitisnonethelessworthpursuing. Thisbookservesamajorreferenceforscientistsandengineersinterestedinapplyingnew fuzzy logic approach tools to achieve intelligent solution in complex systems. It can be also used in special courses of fuzzy logic and artificial intelligence, for researchersand graduatestudents,inadvancecoursesonapplicationsofAIanddecisionsupportsystems. The book thus addresses a rather broad public: logicians, linguists, philosophersas well astheoreticalcomputerscientistsandmathematicians,engineerswithinterestsinlinguistic informationprocessingandtheirapplications. Thebookhassixchapters. Chapter1providestheacademicbackgroundofthedevelopmentoflinguisticvaluedbased intelligentinformationprocess,overviewsandclassifiestheoriesandmethodsinthisdirec- Preface vii tion,alsoreviewsbasicalgebraicconceptsnecessaryforcharacterizationofthelinguistic valuesandforunderstandingthe subsequentchapters,finallyoutlinesthepotentialappli- cations. Chapter 2 starts with a discussion of generallinguistic decision analysis framework, fol- lowedwithonerepresentativelinguisticvaluedapproach,calledthefuzzyordinallinguis- tic approach, a variety of different candidates within this framework especially in terms of aggregationoperatorswill be reviewed. The main focusis givenon the 2-tuple fuzzy linguisticrepresentationmodelasoneofmostpopularfuzzyordinallinguisticapproaches. Formally,theacademicideaoffuzzyordinallinguisticapproachisthatthefinitesetoflin- guisticvaluesisembeddedinalinearorderedstructure. Hence,everylinguisticvaluecan beidentifiedbyanumber,whichservesasanindexofthelinguisticvalue.Theadvantages offuzzyordinallinguisticapproacharemembershipfunctionsassociatedtothelinguistic valuesareunnecessaryinthecomputationprocess. Furthermore,theyarecomputationally simpleandquick. The2-tuplefuzzylinguisticrepresentationmodelinheritsthoseadvan- tages, and provides a better representation and computation scheme to avoid the loss of informationduringthenormalfuzzyordinallinguisticapproach. Asummaryintroduction ofthe2-tuplefuzzylinguisticrepresentationmodelisgivenandsomeofitsapplicationsare alsoprovidedtohelpreadersunderstandthe2-tuplefuzzylinguisticrepresentationmodel. Chapter3introduceshedgealgebrasoflinguisticvalues,inwhichlinguisticrepresentation andmanipulationaremainlyinvestigatedfromthealgebraicpointofview. Theacademic ideaofhedgealgebrasisthatthesetoflinguisticvaluesisembeddedinanaturalandrich enoughalgebraicstructurewithageneralpartiallyorderingdeterminedbynaturalmeaning oflinguisticterms,abasicstructureofuniversalalgebras. Formally,byanalyzinglinguis- tic hedges, one can discover an ordering relation on the set of linguistic values, and the orderingrelation is based on intuitive meaning of linguistic values. Therefore, the moti- vationandfocusofthe researchersinthis directionare todiscoveran algebraicstructure ofterms-domainsoflinguisticvariablesinthecategoryofuniversalalgebras. Thechapter summarizeshedgealgebras, includingthose specializedversion, e.g., symmetricalhedge algebrasandcompletehedgealgebras.Meanwhile,hedgealgebrasareappliedinlinguistic reasoning,constructingmembershipfunctionsoflinguisticvaluesandfuzzycontrol. Chapter 4 introduces linguistic-valued information processing mainly based on a logical algebrastructure- lattice implicationalgebras(LIA).The chapterstarts fromthe general introductionofLIAanditscorrespondinglogicalsystemandapproximatereasoningframe- work. Thelinguistictruth-valuedlatticeimplicationalgebraisdetailedafterwards. Akey viii LinguisticValuesBasedIntelligentInformationProcessing insight behind the linguistic-valued logic scheme is that we can use natural language to expressalogicinwhichthetruthvaluesofpropositionsareexpressedaslinguisticvalues innaturallanguagetermssuchastrue,verytrue,lesstrue,veryfalse,andfalse,insteadof anumericalscale,suchanapproachcouldreduceapproximationerrorsthatcouldestimate membershipfunctionsandcouldalsotreatvagueinformationinitstrueformat. Specially, the set of linguistic truth valuesis embeddedin LIA, which is inspiredfrom hedgealge- bra,establishedbyanalyzingsemanticheredityoflinguistichedges. Basedontheexten- sive work on the LIA based logical system and reasoning approaches, the main research has been focused on studying linguistic representation and manipulation from the logi- calpointofview. BesidestheLIAbasedlinguistic-valuedalgebra,linguistictruth-valued propositionallogic,linguistictruth-valuedautomatedreasoningtheoryandapproaches,lin- guistictruth-valuedapproximatereasoning,andrelevantapplicationsindecisionmaking, knowledge-basedsystemandevaluationarealsosummarized. Chapter 5 introducesfuzzy number indexesof linguistic values. The places of linguistic valuesintheorderedstructureoflinguisticvaluesarerepresentedbyfuzzynumbers.How- ever,itdiffersfromthefuzzysetofthelinguisticvalue,whichexpressesthemembership degreesofobjectsbelongingto thelinguistic value. The advantagesoffuzzynumberin- dexesoflinguisticvaluesarethat(1)incomparablelinguisticvaluesareidentifiedbytheir fuzzynumberindexes;(2)decidingfuzzynumberindexesoflinguisticvaluesisbasedon intuitiveordersoflinguisticvaluesgivenbyindividuals. Hence,theuniverseofdiscourse of linguistic values is not necessary; (3) incomparable linguistic information processing is easily transformedinto numericalcalculus. After a brief introductionof the approach, someapplicationsonestablishingnewaggregationoperatorsindecisionmaking,fuzzyrisk analysis,aswellasinformationgatheringinmulti-agentsystemsarealsohighlighted. Chapter6introducesthehierarchicalstructureanalysisoflinguisticvalues.Themainfocus is on a new frameworkfor linguistic modeling. Formally,for each objectof the domain, thereisacommonorderingoflinguisticvaluessharedbyallindividuals.Linguisticlabels are assumedto bechosenfroma finite predefinedset oflabelsandthe set ofappropriate labelsforavalueisdefinedasarandomsetfromapopulationofindividualsintothesetof subsetsoflabels. Thentheappropriatenessdegree,incontrasttoamembershipdegree,ofa valuetoalabelisderivedfromthatprobabilitydistribution,ormassassignment,ontheset oflabelsubsets.Theframeworkalsoprovidesacoherentcalculusforlinguisticexpressions composed by logical connectives on linguistic labels. Moreover, this helps to construct the formalcontextof linguistic values, obtain linguistic formalconceptsand analyze the Preface ix relation and hierarchical structure among linguistic values. The appropriateness degrees of linguistic values, the formal contextof linguistic values and the hierarchical structure analysisoflinguisticvaluesbasedonformalconceptanalysisarealsosummarized. Chapter7 concludesthebookandlists manyreferencesrelatedtolinguisticvaluesbased intelligent informationprocessing. We hope the book is useful for readers to get a clear pictureofthenewlypresentedtheories,methods,applicationsandfutureresearchdirection aboutlinguisticvaluesbasedintelligentinformationprocessing. ZhengPei,Chengdu DaRuan,Gent&Mol JunLiu,Belfast YangXu,Chengdu
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