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JustificationlWechoosethesocalledxxinourexperimentbecauseithasreceivedwideacceptanceandcanlPrologwaschosenbecauseitoffersawellknownandflexibleenvironmentinwhichfuzzyreasoningmaybeeasilyimplemented.lTherationalebehindthisisthatitcanbemucheasierforanestimatortorateacostashighthantoattempttoplaceadollarvalueontheestimate.lThisstrategyhasbeenwidelyusedinfuzzycontrolapplicationssinceitisnaturalandeasytoimplement.lAfunctiondefinitionexpressesthemembershipfunctionofafuzzysetinafunctionalform,typicallyabell shapedfunction,etc.SuchfunctionsareusedinFLCbecausetheyleadthemselvestomanipulationthroughtheuseoffuzzyarithmetic.lItshouldbenotedthatinourdailylifemostoftheinformationonwhichourdecisionsarebasedislinguisticratherthannumericalinnature.Seeninthisperspective,fuzzycontrolrulesprovideanaturalframeworkforthecharacterizationofhumanbehavioranddecisionsanalysis.lManyexpertshavefoundthatfuzzycontrolrulesprovideaconvenientwaytoexpresstheirdomainknowledge.ThisexplainswhymostFLCsarebasedontheknowledgeandexperiencewhichareexpressedinthelanguageoffuzzy"if the"rule.Chapter4.ExamplesExample/DatalThedatausedinthefollowingexamplewastakenfromanexperimentinwhichxxwasmeasuredbetweenxandxusingaxxtechnique.lThedataconsistsofoverxxmeasurements.lAnexampleofxxisdiscussedandthecontrolrulesofxxarecomparedwithaxxlExamplesofcomplexprocessestowhichthistechniquemaybeappliedarexx,xx,etc.lThefollowingexampleisconstructedonlyforthepurposeofillustratingthecomputationalprocedurediscussed.lThisexampleclearlydemonstratesthattheprofileofanindividualxx,oraverysmallgroupofxx,withnoenoughdatatobestudiedstatistically,canbemeaningfullyanalyzedbyfuzzypossibilisticmethods.lThereisnospaceheretogointodetailonallthesemethods,butdeserveamentionandthebibliographywillpointtodetailedreferencesforthosewishingthislevelofdetail.lNotethatthegolfballspottingexampleisusedthroughoutthepaper.ComparisonslAswell,theprosandconsoftheserepresentationsfromaprocessplanningpointofviewwillbediscussed.lThemethodofusingxxtoimplementxxde
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