不确定性人工智能

Vol.15,No.11©2004JournalofSoftware1000-9825/2004/15(11)1583*1+,2,3,21(,100840)2(,210007)3(,100840)ArtificialIntelligencewithUncertaintyLIDe-Yi1+,LIUChang-Yu2,DUYi3,HANXu21(ChinaInstituteofElectronicSystemEngineering,Beijing100840,China)2(PLAUniversityofScienceandTechnology,Nanjing210007,China)3(ChinaElectronicSystemEngineeringCompany,Beijing100840,China)+Correspondingauthor:E-mail:[e-mail],(11):1583~1594.:Uncertaintyexistswidelyinthesubjectiveandobjectiveworld.Inallkindsofuncertainty,randomnessandfuzzinessarethemostimportantandfundamental.Inthispaper,therelationshipbetweenrandomnessandfuzzinessisdiscussed.Uncertainstatesandtheirchangescanbemeasuredbyentropyandhyper-entropyrespectively.Takenadvantageofentropyandhyper-entropy,theuncertaintyofchaos,fractalandcomplexnetworksbytheirvariousevolutionanddifferentiationarefurtherstudied.Asimpleandeffectivewayisproposedtosimulatetheuncertaintybymeansofknowledgerepresentationwhichprovidesabasisfortheautomationofbothlogicandimagethinkingwithuncertainty.TheAI(artificialintelligence)withuncertaintyisanewcross-discipline,whichcoverscomputerscience,physics,mathematics,brainscience,psychology,cognitivescience,biologyandphilosophy,andresultsintheautomationofrepresentation,processandthinkingforuncertaininformationandknowledge.Keywords:entropy;hyper-entropy;chaos;fractal;complexnetwork;power-lawdistribution:,.,,,,,*SupportedbytheNationalNaturalScienceFoundationofChinaunderGrantNos.60375016,60496323():(1944),,,,,,;(1973),,,;(1971),,,,,;(1978),,,.1584JournalofSoftware2004,15(11),.21.,.:;;;;;:TP18:A?,.:“”,“”.,,,.,[1].,.,,,.,,,,,,..,,..,.,,,.,,,.,,,,,[2].,,.,.,,.,,.,,,.1“”1836•.•,,“,,”.21,,.,,5,.1.1,,,,.,..6,6.,??,,,:1585,.,,,,,.,,.,,.,,,.,.,1933,,,“”“”.,[3]...,,.,.,,,Shortliff,,DempsterShafer,.,.,,.,.1.2.,,,.,,.,.,,.,..,,,,,,,?,,?,?,,,.1965,L.A.Zadeh,.“”,{0,1}[0,1],,[0,1][4].Pawlak[5],GauBuehrerVague[6],.,Vague,.,,.,,.1.3,,.,,,.,,,.,,,1,1586JournalofSoftware2004,15(11).,.,.,.,,,,.,,,[7,8].,Ex,EnHe.“”,,[9].,,,;,,,.,.,,.,[10].,.,,.2,3.2.1.,,.,.“”,,,.,.,,,,.,,“”.,“,”[11~13]..,,.,,,.,..,.,.,,.,.,2090,,,,,,,.:1587,[14].2.22070,Mandelbort.“”,,.,.,,.“”,.,,.,,..,.,.,.,..,,,,,.,,,[15].,.2.3.,..20,ErdosRenyi,.,,,,,.“”.WattsStrogatz1998,..,.,p(k)∝k-g,2g3.,,.,[16].,.,,.20,....,140,.,.,,,[17].,.1588JournalofSoftware2004,15(11)3,,.,.,.3.1,.80%.“”,?1,,.,,.,;,,...2,,...Fig.1Uncertaintyinvisualperception1Fig.2Anopticalperceptionillusion23(a)3(b),3(a),3(b);..,,.,.,.,,,.,,.,,,,[18,19].(a)(b)Fig.3Happyorunhappy?3?.,,0.,,,,,,.,,,.:15893.2,.,.,,.,;,;,,.,,,[19].,,[20],,sigma.4.Fig.4Fadingofafacefrommemory43.3,,,.,.,,,,,,.,,,,.,.4,,,.,;,.,.,,;,.,,[7,8,10],..,.,,,,.,“”“”“”“”,“”“”“”,“”“”“”“”“”“”.Zipf.Zipf:,,P(r)r:P(r)∝1/ra,a,Zipf,a.,a≈1.,“the”2“of”2[21].Zipf,.,.,.Sigma=0Sigma=0.02Sigma=0.04Sigma=0.06Sigma=0.11590JournalofSoftware2004,15(11),..,.,,,,.“”,“”,.Zadeh“computingwithwords”.5,,.:.,,,,,,.,,..5.1,,..5(a)3,,,.,.,10,10,9,…,1,0,1,0.9,…,0.10,.,[8].Fig.5Ashootingexampleofthecloudmodel5,.:,,,.(),,(a)(b)(c):1591,.:(),,;,,;,.3,“,,”.,,3,3.5(b)5(c)10100.,,.,.5.2,,..,,,.,L.,,.R:1.L,L,a°,L*sl(0≤sl≤1)1,b°,L*sr(0≤sr≤1)2.2.1,(a+a)°,L*sl*sl3,(b+b)°,L*sr*sr4;2,(a+a)°,L*sl*sl5,(b+b)°,L*sr*sr6.3.2,M,2(M+1)-1,.,Ra=b=40°,sl=sr=0.7,M=11,6.ExpectationtreeVariation1Variation2Variation3Variation4Variation5Fig.6Simulaterandomvariationsbycloud-transferparameterssets66,Ex={a=b=40°,sl=sr=0.7},5,65.7,R,5,75.En={0.05,0.05,0.1,0.1},He={0.001,0.001,0.01,0.01}.,,.1592JournalofSoftware2004,15(11)ExpectationtreeVariation1Variation2Variation3Variation4Variation5Fig.7Simulaterandomvariationsbycloud-transferrulessets7.,,.,,,.,,,.5.3,.,,;,,.,,,.81,,,.,,,,.9.,,.ExpectationtopologyVariation1Variation2Variation3Variation4Variation5Fig.8Randomsimulationofthecommunicationnetworktopology8:1593ExpectationnetworkVariation1Variation2Variation3Variation4Variation5Fig.9Randomsimulationofthecommunicationnetworktopologyandtraffic96,.,,.,,[22,23].,.“”“”,,,.,,,,.,,,.,,.21,.References:[1]NewtonI;WangKD,Trans.PhilosophiaeNaturalisPrincipiaMathematica.Wuhan:WuhanPress,1992(inChinese).[2]HandyC.BeyondCertainty:TheChangingWorldofOrganization.Pennsylvania:HarvardBusinessSchoolPublishing,1998.[3]WangZK.ApplicationsoftheProbability.Beijing:BeijingNormalUniversityPress,1995(inChinese).[4]LiHX,WangPZ.FuzzySets.Beijing:NationalDefenceIndustryPress,1994(inChinese).[5]PawlakZ.Roughsets.Int’lJournalofComputerandInformationSciences,1982,11(5):341~356.[6]GauWL,BuehrerDJ.Vaguesets.IEEETrans.onSystems,ManandCybernetics,1993,23(2):610~614.[7]LiDY,MengHJ,ShiXM.Membershipcloudsandmembershipcloudgenerators.ComputersResearchandDevelopment,1995,32(6):16~21(inChinesewithEnglishabstract).[8]LiDY.Uncertaintyinknowledgerepresentation.EngineeringScience,2000,2(10):73~79(inChinesewithEnglishabstract).[9]QiuWH.ManagementSupportandAppliedEntropy.Beiji