Fussy Set Theory.ppt

FussySetTheoryDefinitionAfuzzysubsetAofauniverseofdiscourseUischaracterizedbyamembershipfunctionwhichassociatewitheachelementuofUanumberintheinterval[0,1].SetTheory:A={a,b,c}.SubsetofA:{a,c}.(universe)Therearethreebasicoperations:AB={elementsinAorinB}.AB={elementsinbothAandB}NotA=U-,AandBbetwofussysubsetsofU,,,FuzzyInformationRetrievalWefirstsetupterm-termcorrelationmatric:Fortermskiandkl,Whereniisthenumberofdocumentscontainingki,nlisthenumberofdocumentscontainingklAndni,,i=,adocumentdjhasadegreeofmembershipputedasExample:c1,2=,c1,3==(0,1,1,0).1,1=1-*=(1,0,0,0).1,2=1-0.(sincec1,1=1.)Howisd3=(1,0,1,0)?FuzzyInformationRetrievalWhenever,thedocumentdjcontainsatermthatisstronglyrelatedtoki,thenthedocumentdjisbelongtothefuzzysetoftermki,.,i,,c1,2=,d1=(0,1,0,0).1,1=1-(1-)=:QueryisaBooleanformula,.,q=Kaand(KbornotKc).q=(1,1,1)or(1,1,0)or(1,0,0)..q,:=(1,0,1,0),d2=(1,1,0,0),andd3=(0,1,1,0).(putetheterm-termcorrelationmatrixci,j.(putei,j(membershipofdocumentjintermi.)(3)Ifthequeryq=(1,0,0,0)or(1,1,0,0),computeq,kforeachdocumentdk.