简介:Conceptlatticeisapowerfultoolfordataanalysis.Ithasbeenappliedwidelytomachinelearning,knowledgediscoveryandsoftwareengineeringandsoon.Someaspectsofconceptlatticehavebeenstudiedwidelysuchasbuildinglatticeandrulesextraction,asforitsalgebraicproperties,therehasnotbeendiscussedsystematically.Thepapersuggestsabinaryoperationbetweentheelementsforthesetofallconceptsinformalcontext.Thisturnstheconceptlatticeingeneralsignificanceintothosewithoperators.Wealsoprovedthattheconceptlatticeisalatticeinalgebraicsignificanceandstudieditsalgebraicproperties.Theseresultsprovidedtheoreticalfoundationandanewmethodforfurtherstudyofconceptlattice.
简介:GivenastablematrixA∈Cn×n,therearesomesimplesimultaneousinequalitieswhosecoefficientsrelyonA.For(?)PH=P∈Cn×n,ifPsatisfiestheseinequlities,thenPA+AHP<0.Asanapplicationofthemainresults,thestabilityofthematrixfamilyistreated.Besides,somegeometricpropertiesofthesetofalltheLyapunovmatricesofagivenstablematrixareconsidered.