Fuzzy Logic: Recent Applications and Developments PDF
Preview Fuzzy Logic: Recent Applications and Developments
Jenny Carter Francisco Chiclana Arjab Singh Khuman Tianhua Chen Editors Fuzzy Logic Recent Applications and Developments Fuzzy Logic · · Jenny Carter Francisco Chiclana · Arjab Singh Khuman Tianhua Chen Editors Fuzzy Logic Recent Applications and Developments Editors JennyCarter FranciscoChiclana DepartmentofComputerScience FacultyofComputing UniversityofHuddersfield EngineeringandMedia Huddersfield,UK DeMontfortUniversity Leicester,UK ArjabSinghKhuman FacultyofComputing TianhuaChen EngineeringandMedia DepartmentofComputerScience DeMontfortUniversity UniversityofHuddersfield Leicester,UK Huddersfield,UK ISBN978-3-030-66473-2 ISBN978-3-030-66474-9 (eBook) https://doi.org/10.1007/978-3-030-66474-9 ©SpringerNatureSwitzerlandAG2021 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Many problems within industry and commerce can be modelled mathematically and/or statistically. However, in practice, applications modelled in this way often performpoorly.Implementedassumptionscancausedevelopedsolutionstolacka certain level of robustness. Standard control applications, for example, often work poorlyundercertainconditionsortheyarenotsmoothintheirmovement.Physical measurementsare,bytheirnature,imprecise.Theyareonlyasgoodastheinstrument doingthemeasuring.A2Kgbagofsugarisnever‘exactly’2Kgforexample.Yet, traditionalmathematicallybasedcontrolsolutionsusesuchmeasurementsasbeing precise. Experts make decisions with imprecise data in an uncertain world. They work with knowledge that is rarely defined mathematically or algorithmically but usesvagueterminologywithwords. Fuzzy logic relies on the concept of a fuzzy set, which was proposed by Lotfi Zadeh, in his 1965 seminal paper—‘Fuzzy Sets’ (published in Information and Control,volume8,pp.338–353).ZadehwasaProfessorattheUniversityofSouthern California until his death in 2017. The idea of fuzzy sets described in his seminal work lays the basis for Fuzzy Logic. Fuzzy Logic is particularly good at handling uncertainty,vaguenessandimprecision.Thisisveryusefulwhereaproblemcanbe describedlinguistically(usingwords)or,aswithneuralnetworks,wherethereisdata andyouarelookingforrelationshipsorpatternswithinthatdata.FuzzyLogicuses imprecisiontoproviderobustsolutionstoproblems.Applicationsoffuzzylogicare variedandincluderobotics,washingmachinecontrol,nuclearreactors,information retrieval,trainscheduling,systemmodelling,camerafocus,stocktracking. Thechaptersinthisbookprovidefurtherinsightintothewiderangeofapproaches to problem-solving using fuzzy logic and illustrate these approaches over a wide varietyofapplicationareas. TheEditors Huddersfield,UK JennyCarter Leicester,UK FranciscoChiclana Leicester,UK ArjabSinghKhuman Huddersfield,UK TianhuaChen v Contents FuzzyLogic,aLogician’sPerspective ............................... 1 PatrickFogarty AFuzzyApproachtoSentimentAnalysisattheSentenceLevel ........ 11 OrestesAppel,FranciscoChiclana,JenniferCarter,andHamidoFujita ConsensusinSentimentAnalysis .................................... 35 OrestesAppel,FranciscoChiclana,JenniferCarter,andHamidoFujita FosteringPositivePersonalisationThroughFuzzyClustering .......... 51 RaymondMoodley DiagnosingAlzheimer’sDiseaseUsingaSelf-organisingFuzzy Classifier ......................................................... 69 JonathanStirling,TianhuaChen,andMagdaBucholc AutismSpectrumDisorderClassificationUsingaSelf-organising FuzzyClassifier ................................................... 83 JonathanStirling,TianhuaChen,andMariosAdamou AnOutlierDetectionInformedAggregationApproachforGroup Decision-Making .................................................. 95 ChunruChen, TianghuaChen, ZhongminWang, YanpingChen, andHengshanZhang Novel Aggregation Functions Based on Domain Partition withConcentrateRegionofData .................................... 107 HengshanZhang,TianhuaChen,ZhongminWang,andYanpinChen ApplyingFuzzyPatternTreesfortheAssessmentofCornealNerve Tortuosity ........................................................ 131 PanSu, XuanhaoZhang, HaoQiu, JianyangXie, YitianZhao, JiangLiu,andTianhuaChen AMamdaniFuzzyLogicInferenceSystemtoEstimateProjectCost .... 145 DanielHelderMaiaandArjabSinghKhuman vii viii Contents Artificial Intelligence in FPS Games: NPC Difficulty Effects onGameplay ...................................................... 165 AdamHubble,JackMoorin,andArjabSinghKhuman AdaptiveCruiseControlUsingFuzzyLogic .......................... 191 NathanLloydandArjabSinghKhuman Automatic Camera Flash Using a Mamdani Type One Fuzzy InferenceSystem .................................................. 221 SophieHughesandArjabSinghKhuman The Application of Fuzzy Logic in Determining Outcomes ofeSportsEvents .................................................. 235 SpencerDeaneandArjabSinghKhuman WaterCarbonationFuzzyInferenceSystem ......................... 253 WilliamChapmanandArjabSinghKhuman Fuzzy Logic, a Logician’s Perspective PatrickFogarty Abstract Fuzzylogicarisesfromanattempttomanagetheinherentvaguenessthere isinthelanguageweusewhendiscussingourworld—itisaformaltreatmentofvague predicates.Thischapterwilldescribehowthisformalstructurehascomeabout,from origins in philosophical thought, through the development of non-standard logics. Itwillexplore,fromalogician’sperspective,usefultoolsusingfuzzysettheories, such as Basic Fuzzy Logic (BL) and T-Norm Fuzzy logics, deployed in computer systemstoday.Itisintendedtodetailthetechniquesusedtosetupsuchtheoriesand toreviewtherelationshipthatLogicbearstothem.Inconclusion,itisproposedthat furthersuggestedtheoreticalinvestigationsmightyieldusefulpracticalresults. · · · · · · Keyword Aristotle Axiomatization BL Eubulides Fuzzylogic Hájek · · · · · History Logic Logician’sperspective Settheories Sorites Suggested · · · · theoreticalinvestigations T-norms Vagueness Wang’sparadox Zadeh 1 Introduction ThesubjectofthischapteristhefoundationsofFuzzySetTheoryandFuzzyLogic. Whenapplyingtechniquesincomputerscienceitisnotnecessarytoknowtheirhistor- icaldevelopment.Likedrivingacar,itisnotnecessarytounderstandtheworkingsof theinternalcombustionengine.Ontheotherhand,understandingenginesandtheir historycanenhanceourdrivingexperienceandonegainsabroaderappreciationof the car as an object created by human endeavour. Similarly, when we stand back and view Fuzzy Logic from a historical perspective, by examining its foundations wegainanoverviewthatincreasesourabilitytoseerelationships,andallowsusto exploreoptionsforfutureinnovation.Thischapterisintendedtogivethereadera paththroughtheliteraturetohelpgainahistoricalperspective.Thisisnotintended tobeacomprehensivereview,rathertoinspirefurtherreading;[1]asinglesource textcoveringthehistoricaldevelopmentofFuzzySetTheoryandFuzzyLogic,isa B P.Fogarty( ) Doora,Portmagee,Co.KerryV23RX94,Ireland ©SpringerNatureSwitzerlandAG2021 1 J.Carteretal.(eds.),FuzzyLogic, https://doi.org/10.1007/978-3-030-66474-9_1 2 P.Fogarty goodplacetostart.Myconclusions proposesome‘bluesky’ideaswhichareulti- mately intended to pique interestand encourage further thought. As with somany othersubjects,itallstartswiththeGreeksandAristotle. 2 AncientGreece AristotleinhisMetaphysicsbookIVPage15977:23[2]presentsaformulationof thelawoftheexcludedmiddle: Butontheotherhand,therecannotbeanintermediarybetweencontradictories,butofone subjectwemusteitheraffirmordenyanyonepredicate. Aristotle was aware that there are things that are indeterminate or at least problematicwhentryingtodeterminetruthorfalsity. Whatis,necessarilyis,whenitis;andwhatisnot,necessarilyisnot,whenitisnot.Butnot everythingthatis,necessarilyis;andnoteverythingthatisnotnecessarilyisnot…Imean, forexample:itisnecessaryfortheretobeornottobeasea-battletomorrow;butitisnot necessaryforasea-battletotakeplacetomorrow,norforonenottotakeplace—thoughitis necessaryforonetotakeplaceornottotakeplace…Clearly,thenitisnotnecessaryofevery affirmationandoppositenegationoneshouldbetrueandtheotherfalse.Forwhatholdsfor thingsthataredoesnotholdforthingsthatarenotbutmaypossiblybeornotbe;withthese itisaswehavesaid.Barnes[2]DeInterpretationePage309:23 ThisisaquitebrilliantanalysisandshowshowAristotleunderstoodcontingency andrecognisedthatthereisasubtletyintheanalysisoftruthandfalsitywhenconsid- ering indeterminate predicates. Unfortunately, Aristotle never pursued the issues muchfurther.ThedevelopmentofLogicscapableofaddressingthequestionofpre- determinationarisingfromAristotle’sanalysishadtowaituntilŁukasiewiczinthe twentiethcentury.Themotivationforhismultivaluedlogicswaspreciselytoremove thedependenceoflogiconnecessity: Even then Istrove toconstruct non-Aristotelian logic,but in vain. Now I believeIhave succeededinthis.Mypathwasindicatedtomebyantinomies,whichprovethatthereis a gap in Aristotle’s logic. Filling that gap led me to a transformation of the traditional principlesoflogic.Examinationofthatissuewasthesubject-matterofmylastlectures.I haveprovedthatinadditiontotrueandfalsepropositionstherearepossiblepropositions,to whichobjectivepossibilitycorrespondsasathirdinadditiontobeingandnon-being.This gaverisetoasystemofthree-valuedlogic,whichIworkedoutindetaillastsummer.That systemisascoherentandself-consistentasAristotle’slogic,andismuchricherinlaws andformulae.Thatnewlogic,byintroducingtheconceptofobjectivepossibility,destroys the former concept of science, based on necessity. Possible phenomena have no causes, althoughtheythemselvescanbethebeginningofacausalsequence.Anactofacreative individualcanbefreeandatthesametimeaffectthecourseoftheworld.Simons[3]Sect.5.2 ‘IndeterminismandtheThirdValue’ Aristotlepresenteduswithaversionoflogicalformalism,syllogisticorclassical logic,whichcannothandlevagueconcepts.Thevagueisdismissedfromthelogical framework and not addressed in Aristotle’s logic. His contemporary Eubulides, in FuzzyLogic,aLogician’sPerspective 3 contrast,consideredsemanticparadoxesandfoundtheminterestingtoexplore[4]. Aristotle and Eubulides illustrate that, from the very beginnings of philosophical thought,thinkershavebeenawareofpredicativevaguenessandhavetriedindifferent waystoaddressit. Eubulidesspecificallystudiedthetypeofsemanticvaguenessmanifestedinthe “Sorites” paradox—a paradox conceived or at least popularised by him in the 4th centuryBCE.ThenamecomesfromtheGreekσωρει´αmeaningheap.TheSorites paradoxasks,“whendoesacollectionofgrainsofsandbecomeaheap?”Obviously, youcannotreasonablycallonegrainofsandaheap,nortwo,northree;perhapsa thousand grains? When is it exactly that a collection of grains of sand becomes a heap?Theanswertothequestionisvague-itisnotclearthatthereisadefinitive answer. MoreformallythisparadoxcanbestatedfollowingWang’sparadoxasin[5]: if nis small then n+1 is small 0issmall ∴all numbers are small by mathematical induction InthecaseofEubulides’Soritesparadox,thepredicateheapisvagueandinthe case of Wang the predicate small is vague. This creates a problem when trying to correctlyassigntruthtoaproposition.Aristotle’scontentioninproposingthelawof theexcludedmiddleisthatapropositionmusteitherbetrueorfalseandthatthere isnootherpossibility. In classical logic, truth is a bivalent attribute of a proposition. A proposition is either true or false—there are no other options. This does not allow for vague concepts,whichofitselfisnotabadthing;takingthisrouteallowsthedevelopment oflogicforwell-definedpredicateswithnovagueness,butitinhibitsdiscussionof propositionsthatcontainvaguepredicates. Aristotlehaddetermined,inhisdiscussionofthesea-battle,thatforfutureevents thelawoftheexcludedmiddledidnotapply[2]DeInterpretationePage309:30.Itis notthatAristotleandclassicallogiciansdidnotknowofvaguenessandthesemantic paradoxes that arise, rather they could see no useful way to implement a logic to processpropositionscontainingvagueorindeterminatepredicates.Ananalogycan bedrawnbetweentheemergenceofnon-Euclideangeometriesandthearrivalofnon- classicallogics.Itwasnotuntilnewaxiomatisationsforsettheoriesandlogicsthat vaguenesscouldbeexploitedinapracticalway.Non-Euclideangeometriesbeganto beworkedoninthe1820sbyBolyaiandLobachevsky[6]Chap.3Sects.30and31. By1882,Pasch[7]hadpublishedanaxiomatizationanddemonstratedthepowerof axiomaticstoproducedeductivegeometries.Theapplicabilityofaxiomaticstoother areasofmathematicswasseentobeausefultoolbyHilbert[7]anditwasHilbert’s visionthatsetthestagefordevelopmentsinsettheoryinthetwentiethcentury,and ultimatelytothedevelopmentoffuzzysettheoryandfuzzylogic.
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