粒计算研究综述

26Vol.2.6200712CAAITransactionsonIntelligentSystemsDec.2007王国胤1,2,张清华1,2,胡军1,3(1.重庆邮电大学计算机科学与技术研究所,重庆400065;2.西南交通大学信息科学与技术学院,四川成都610031;3.西安电子科技大学电子工程学院,陕西西安710071):(granularcomputing).,.,,,,.:;;;;;:TP18:A:16734785(2007)06000819AnoverviewofgranularcomputingWANGGuoyin1,2,ZHANGQinghua1,2,HUJun1,3(1.InstituteofComputerScience&Technology,ChongqingUniversityofPostsandTelecommunications,Chongqing400065,China;2.SchoolofInformationScience&Technology,SouthwestJiaotongUniversity,Chengdu610031,China;3.SchoolofElectronicEngineering,XidianUniversity,Xian710071,China)Abstract:Inthefieldofcomputationalintelligence,granularcomputing(GrC)isanewwaytosimulatehumanthinkingtohelpsolvecomplicatedproblems.GrCinvolvesallthetheories,methodologiesandtechniquesofgranularity,providingapowerfultoolforthesolutionofcomplexproblems,massivedatamining,andfuzzyinformationprocessing.Inthispaper,firstthecurrentsituationandthedevelopmentprospectsofGrCareintroduced,thenthefundamentalandexistingproblemsrelatedtoGrCarepresentedanditsbasicmodelsandmethodssummarized.Finally,somefutureresearchtopicsaboutGrCarepresented,suchas,uniformgranularcomputingmodel,granulationofcomplexproblemspace,transformationbetweengranulespaces,efficientgranularcomputingalgorithm,novelgranularcomputingmodel,dynamicgranularcomputingmodel,datadrivengranularcomputingmodel,fuzzygranularcomputingmethod,andtheapplicationsofgranularcomputingmodels,etc.Keywords:granularcomputing;datamining;intelligentinformationprocessing;roughsets;fuzzysets;quotientspace:20070402.:(60573068);;(KJ060517).Zadeh1979!Fuzzysetsandinformationgranularity∀[1],.Zadeh,.!∀!∀!∀DS!∀.Hobss1985!(granularity)∀[2],,,.Lin1988[3].1996,UCBerkeley,Zadeh!granularcomputing∀,Zadeh!granularmathematics∀,Lin!granularcomputing∀,GrC.[4-10],(Rough),,,.,,1990,,[11-12].1997,Zadeh[13],3:.,,,.,(),,.,,.Lin,Yao[14-16],[17-22],,ifthen,,.,Yao.Yao3[22]:1),;2),;3),.,.,Skowron[23-27]RoughRough.[28-30]Rough,-(G),,.,,,2003,,,[31-35].2002[36],,.[37],,,.[38-44],,,,.[45-47],,,,.[48],,,,,,,.Zhang[49-50],.[51],.[52][53],,,,.Yager[54].Lin[55]2006!infrastructuresforAIengineering∀.,BargielaPedrycz[56].Yager,[57].1粒计算的基本组成3:#9#6,:.11[58-59],.,,,(),,.,..,.!∀,,!∀[59].12,.,..,.,.,,,.(),().,.13,,.,[20]..()[20]3:...,.,,.,(),.,,.,;,,.,.2粒计算的基本问题2,.,,..,,.21,,,.,.,..()()()[59].,2..,.,,,.,,.,,.,.#10#2,,()()2.,,,,Hasse.().,,,.,(),.22,.,2,,2[59]:,.,,...,.;;.,,,.,,,,.!∀!∀!∀,,.2,,.,.,,[17],[1],[35],[60],[3].,,,.!∀,,[59].,.3粒计算的主要模型与理论方法31,!∀,[61].,,,,.(),,.,∃∃∃Zadeh.,.,.,!ifthen∀.(computingwithwords)[62].,.,,,.2.();,#11#6,:[63].,[62].2:,.(informationgranulation).,,,.,,,..[64-65](theoryoffuzzyinformationgranulation,TFIG),,.Zadeh[64],,,.Zadeh,,Wang[66].,,[67-68],,,(IGCW),,.,,,.,;,.,.,,.,,,.,;,,,,.,,[69-72].Wang,(linguisticdynamicsystems,LDS),[37],,,,.,.,,,,.32,,Pawlak[73]2080,(),(),().,2().,,,.XXR.X/RUR,[x]Rx,x%U.Pawlak(X,R),X(U).(X,R),,:R-(X)={x%U|[x]RX}R-(X)={x%U|[x]R&X∋}.R-(X)∋R-(X),X,!∀..(softcomputing)Zadea[61-65].,;,.,20,,,[74-75].#12#2.,.,.,2:,Rough.3[63]:1);2);3).3(),,.Kryszkiewicz[76],Stefanowski[77].[78]2,,:2,,,.[79],,,,.,,,.,,(U/R)U/R,(2U,~,n,U),(U,(U/R)).[80],,,.,Rough[81].Pawlak[82]Rough,,.PolkowskiSkowron[83]RoughMereology,,Rough(RNC),(),.Skowron[84][83],,,,,.,,Agent,.Peters[85],,,2,.Peters[86]RNC.Lin[3-4]Rough,,Rough,,Fuzzy,[87].Yao[88],,,,.Rough,[28-30].33,[11-12],!,.,,,.,∀.,,,.[11].,,#13#6,:[31,34,89-94].,(X,F,T).,X,F,TX.,R(),R([X]),([X],[F],[T]),R..,,2:!∀!∀.!∀,.!∀,2,.2.2X1X2,,!∀,X3.X1X2s1s2,,X3s1s2.s1s2,s1s22.!∀!∀.,!∀,:,X1-a.,Xd,[X]d.,[35],.,..,,.,,.,3:1)X;2)T;3).:,;,..,[31,34,89-95],,,,,,,,,!∀!∀2,.,,,,.,.343.3,,,,.341基于划分的粒计算模型Yao[17],2,,.,,,.2:ZoominginZoomingout.2,.342基于覆盖的粒计算模型Lin,[3-10],..Zhu[96-97],2,,,.[98].[99],,ZoominginZoomingout2#14#2.343基于容差关系的粒计算模型,,.,,,,.,.[38-39],,,,.[46-47,59],.344基于概念格的粒计算模型,,Wille1982[100],,..,,,,.,,Hasse,.[101].[102-103],,,,,.[104]:,.,;,.,.2:,;,.,,,.,.,,Yao[17]((DL)(m(),,).[105]3:GMGM,3,.,[102-103],.,,[49-50][106].,.4粒计算模型之间的关系.,,.!∀(),.,3,.,.3.,.,,.,,#15#6,:,.,[75].,,,,,.,(),,,(),,().!∀,.,[107].,,!∀,!∀,.(),,,.,.,,.,,..(),.(),.,,!∀,,..,3:000.(),,..,.,,.,,,,,,,.,,,.,,,(),,,.().,,,,,.,.!∀,.().,2[108].,.Dubois[109],[110-111],.[35],()(),..[112],,Fuzzy.[113],().,,,,,,.,#16#2,.,,,.,..,,.,.2(),ZoominginZoomingout2().,,.,,.,,.[49-50].5粒计算的应用研究,..51,.,[31,114].,,,..Zadeh,Pedrycz[115],,.,HirotaPedrycz[116],,.Nobuhara[117],.[118-119],,.[31,114,120],,.52,.,..,..,..,.,,,,,[48].,BellmanKalabaZadeh1966,,.,[48],.,,..,.2[121]:,;[122-124]..,#17#6,:,,,,.[91],,,.Apriori,.[125].!∀,,,!∀..53,,,.,,[95].,.,.,,[89-91,126-127].,,,,[63].,,.,,2070,80,.,[92-93].,[30,128](DSBVS),.,Zhang[49-50],.,[129],.[130],Skowron,.,Wang[37].,[94],,.,,,,.6粒计算研究的展望,,,.,,,..61,,.,;(),;,..,,.,.62.,.,.,,.,,,,.,#18#2,...,,.,,.,,.,,.,.[131-132],,,,.63.,,.,,.!∀!∀,...,ZoominginZoomingout2.,,,,.,,,.!∀,.!∀!∀!∀!∀,,.!∀!∀,,.64.,,,.,.,O(n2).,.O(n1.5)O(nlgn),,.65,.,,,.,,,,.,[35].,[108-111].,2,.,,,,.,.66,()....67.,#19#6,:,.,,.[131-132],,Skowron,,,..,,(),,,()..,,,.68,.,!∀.,,.,Zadeh,.,,,.,,.,DS.,.,,,.(),,,,.,,.,.,.69,,.,..,,.,.,,.,.,,.,,,,.,,,.7结束语,,,.,,#20#2.,,,,..:[1]