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1、2012/5/22管理中的模糊信息处理EugeneLevnerBarIlanUniversity,IsraelHaoHuShanghaiJiaoTongUniversityOperationalResearchatSJTUShanghaiNovemberDecember2010Whatisafuzzyset?Whatisfuzzylogic?Whatisafuzzynumber?Howweconstructafuzzyexpertsystem?12012/5/22FuzzyDataandFuzzySetsThreetypes
2、ofdata:•Exact(thesortingproblem)•Probabilistic(theexpectedprofit)•Fuzzy(athickbook,ayoungperson,agoodstudent)MotivationforFuzzyLogic•Paradox1.“SORITES”–TheParadoxoftheHeap•Takeagrainofsandfromaheapandyouwillstillhaveaheap.Takeanothergrainfromit,anditremainsaheap,an
3、dsoon.Eventuallyonegrainisleft.Itisnotaheap.Whendidtheheapceasebeingaheap?22012/5/22MotivationforFuzzyLogic•Paradox1.“SORITES”–TheParadoxoftheHeap•Takeagrainofsandfromaheapandyouwillstillhaveaheap.Takeanothergrainfromit,anditremainsaheap,andsoon.Eventuallyonegraini
4、sleft.Itisnotaheap.Whendidtheheapceasebeingaheap?MotivationforFuzzyLogic•Paradox1.“SORITES”–ParadoxoftheHeap•Takeagrainofsandfromaheapandyouwillstillhaveaheap.Takeanothergrainfromit,anditremainsaheap,andsoon.Eventuallyonegrainisleft.Itisnotaheap.Whendidtheheapcease
5、beingaheap?32012/5/22MotivationforFuzzyLogic-2Paradox2.Falakros–TheParadoxoftheBaldHead•Pluckahairfromanormalman’sheadandhedoesnotsuddenlybecomebald.Pulloutanother,andathird,andaforth,andhestillisn’tbald.Kepppluckingandeventuallythewincingmanwillhavenohairsatallonh
6、ishead.Whendidhebecomebald?•Ifanumberxissmallthanx+1isalsosmall.Ifx+1smallthanx+1+1issmalltoo.Thereforebyinduction,1,000,000isasmallnumber.(TheHaoWangParadox)MotivationforFuzzyLogic3•Paradox3.ParadoxofTheseus’sShip•"WhenTheseusreturnedfromslayingtheMinotaur,saysPlu
7、tarch,theAthenianspreservedhisship.Asplanksrotted,theyreplacedthemwithnewones.Whenthefirstplankwasreplaced,everyoneagreeditwasstillthesameship.Addingasecondplankmadenodifferenceeither.Atsomepoint,theAthenianshavereplacedeveryplankintheship.Wasitadifferentship?Atwha
8、tpointdiditbecomedifferent?"42012/5/22MotivationforFuzzyLogic-4Paradox4.TheHaoWangParadox[王浩美籍华人]•Ifanumberxissmallthenx+1isalsosmall.Ifx+1smallt
