Table Of ContentATLANTIS COMPUTATIONAL INTELLIGENCE SYSTEMS
VOLUME 1
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AtlantisComputational Intelligence Systems
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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
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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
