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Studies in Computational Intelligence 1040 María Eugenia Cornejo István Á. Harmati László T. Kóczy Jesús Medina-Moreno Editors Computational Intelligence and Mathematics for Tackling Complex Problems 4 Studies in Computational Intelligence Volume 1040 SeriesEditor JanuszKacprzyk,PolishAcademyofSciences,Warsaw,Poland The series “Studies in Computational Intelligence” (SCI) publishes new developments and advances in the various areas of computational intelligence—quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as themethodologiesbehindthem.Theseriescontainsmonographs,lecturenotesand editedvolumesincomputationalintelligencespanningtheareasofneuralnetworks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems,andhybridintelligentsystems.Ofparticularvaluetoboththecontributors and the readership are the short publication timeframe and the world-wide distribution,whichenablebothwideandrapiddisseminationofresearchoutput. ThisseriesalsopublishesOpenAccessbooks.ArecentexampleisthebookSwan, Nivel, Kant, Hedges, Atkinson, Steunebrink: The Road to General Intelligence https://link.springer.com/book/10.1007/978-3-031-08020-3 IndexedbySCOPUS,DBLP,WTIFrankfurteG,zbMATH,SCImago. AllbookspublishedintheseriesaresubmittedforconsiderationinWebofScience. · · María Eugenia Cornejo István Á. Harmati · László T. Kóczy Jesús Medina-Moreno Editors Computational Intelligence and Mathematics for Tackling Complex Problems 4 Editors MaríaEugeniaCornejo IstvánÁ.Harmati FacultyofEngineering DepartmentofMathematics DepartmentofMathematics andComputationalSciences UniversityofCádiz SzéchenyiIstvánUniversity PuertoReal,Spain Gyo˝r,Hungary LászlóT.Kóczy JesúsMedina-Moreno FacultyofEngineeringSciences ScienceFaculty SzéchenyiIstvánUniversity DepartmentofMathematics Gyo˝r,Hungary UniversityofCádiz Cádiz,Spain ISSN 1860-949X ISSN 1860-9503 (electronic) StudiesinComputationalIntelligence ISBN 978-3-031-07706-7 ISBN 978-3-031-07707-4 (eBook) https://doi.org/10.1007/978-3-031-07707-4 ©TheEditor(s)(ifapplicable)andTheAuthor(s),underexclusivelicensetoSpringerNature SwitzerlandAG2023 Thisworkissubjecttocopyright.AllrightsaresolelyandexclusivelylicensedbythePublisher,whether thewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuse ofillustrations,recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,and transmissionorinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilar ordissimilarmethodologynowknownorhereafterdeveloped. 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ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Thetoolkitofferedbyclassicalmathematicshasundeniableandprovensuccessesin awiderangeofapplications.Nevertheless,therearemoreandmoreproblemsinreal life that require at least approximate solutions. In many cases, the classical math- ematical discussion is absolutely hopeless, due to high complexity, uncertain and oftenconfusing(partiallycontradictory)information.Moreover,inmanysituations, finding the exact model needs tremendous effort and usually, there is no hope for propermodelidentificationandvalidationintheclassicalsense.Althoughinsome casesthemainstream(classic,symbolic)artificialintelligencemayprovidefeasible solutions, it usually works only with a sufficiently large collection of representing data,whichcanbeagreatbarrierinreallife,especiallyinhuman-influencedprob- lems.Ontheotherhand,weallexperiencethatMotherNaturemayprovidevarious effectivesolutionsforverycomplexproblems.Thus,mimickingthestructureorthe behaviourofanimalsoragroupofanimals,orotherlivingcreatures,ormodelling human thinking can be a way to a possible solution. Computational Intelligence involves such methods and offers highly competitive solutions to very complex, real-lifeproblems.Besidesthesesuccesses,themainlanguageofCIremainsMath- ematics,andinteractionsofmathematicalthinkingwithCIoftenunveilinteresting, deepconnectionsandenlightenthetheoreticalbackgroundofpracticalCImethods.1 The European Symposium on Computational Intelligence and Mathematics (ESCIM)annuallyensurestheopportunityofsharingideasbetweenCIresearchers and mathematicians. In 2021, the symposium took place in Budapest, Hungary, at a time when the current COVID-19 situation made personal attendance possible. Thisvolumecontainsthefulltextsofasetofselectedpapersfromtheconference. We acknowledge the work given by the Program Committee members, reviewers, authors, local organizers and the support of the 2014–2020 ERDF Operational Programme in collaboration with the State Research Agency (AEI) in project 1Partiallysupportedbythe2014-2020ERDFOperationalProgrammeincollaborationwiththe StateResearchAgency(AEI)inprojectPID2019-108991GB-I00, theDepartmentofEconomy, Knowledge,BusinessandUniversityoftheRegionalGovernmentofAndalusiainprojectFEDER- UCA18-108612,bytheNationalResearch,DevelopmentandInnovationOffice(Hungary)grantnr. K124055andbytheEuropeanCooperationinScience&Technology(COST)ActionCA17124. v vi Preface PID2019-108991GB-I00, the Department of Economy, Knowledge, Business and theUniversityoftheRegionalGovernmentofAndalusiainprojectFEDER-UCA18- 108612, by the National Research, Development and Innovation Office (Hungary) grant nr. K124055, and by the European Cooperation in Science & Technology (COST)ActionCA17124participation. Inthenext,thepaperswillbebrieflydescribed. The first paper discusses a purely theoretical topic, namely, it examines Gödel S4logic.Theauthorsintroducesemanticsforthecrispandthefuzzycasebasedon birelationalframesandshowthattheselogicshavethefinitemodelproperty.Conse- quently,boththecrispandfuzzyversionsofGödelS4modallogicsaredecidable. Themainideaofthiswork(thebirelationalinterpretation)mayprovideatheoretical basisfortheanalysisofotherGödelmodallogicswhosedecidabilitywaspreviously unknown. ThesecondpaperpresentsacomparisonbetweenMulti-adjointlogicandBasic logic,provingthattheaxiomsgiveninMulti-adjointlogicareprovableformulasin Basiclogic,aswellasanalysingdifferentaxiomsofBasiclogicthatcannotbeproven inMulti-adjointlogic.ThetranslationofaxiomsofBasiclogictoMulti-adjointlogic isalsostudied.TheauthorsconcludethatMulti-adjointlogicisamoregenerallogic thanBasiclogic,consideringaweakeraxiomatization. The third paper focuses on the study of the immediate consequence operator, whichplaysakeyroleinthesemanticsofmulti-adjointlogicprogrammingframe- work. Specifically, the authors have provided a generalization of the immediate consequenceoperatorbasedongeneralizedquantifiers,showingthatthisnewoper- ator is monotonic. This monotonicity property is fundamental for the fixed-point semanticsofthelogicprogrammingframework. The fourth paper introduces a unified approach to the theory of forward and backwardoperatorsinducedbyL-fuzzyrelations.Theauthorsillustratetheroleof these operators in theory of generalized fuzzy rough sets, in the study of oriented fuzzyconceptlatticesandfuzzymorphology. Inthefifthpaper,theauthorsexplorethereductionsofobjectsandattributesin RoughSetTheory.Focusingontheinformationtables,theauthorsprovidedifferent propertiesaboutbireductsaswellasitsrelationshipwithreducts.Theyalsoanalyse specialcasesofbireductssuchaswhenthesetofobjectsorattributesarethewhole setofobjectsorattributesorwhentheyaretheemptyset. Thesixthpaperisdevotedtoanovelmethodinmedicalimageprocessing.Lesions growingintheliverareroundish,buttheirregularityoftheshapeisquitecommon, so the classical (crisp) Hough transform often fails to identify these objects. To handle these not perfectly circular patterns, the authors propose the application of the fuzzy Hough transform. They examine the effect of median filtering on fuzzy Houghtransform,namely,analysingtheeffectofvariouskernelsizes.Moreover,the effect of the shape of the membership function applied in the fuzzification step is investigated,too,givingsomeinsightintothesensitivityofthemethod. Preface vii In the seventh paper, the author examines some directional properties of semi- aggregationfunctions,namelythedirectionalmonotonicityandthedirectionalshift- invariantness.Theirrelationtothedirectionalderivativesisalsoexplainedandillus- tratedbyseveralexamples.Theresultspresentedinthepapergiveanewviewpoint topre-aggregationfunctionsandprovideanovelgeneralizationoftheclassicalshift- invariantnessoffunctions.Fromthepracticalpointofview,thesefindingsmaybeof interestinseveralfields,forexample,infuzzyrule-basedsystems,imageprocessing andmeasurementtheory. Theimportanceofaggregationfunctionsiswellknownandstraightforward.The eighthpaperpresentsanewconstructionmethodtoaggregationfunctionsonbounded lattices,whichisageneralizationofthePhi-transformand(cid:2)F,c(cid:3)-transformation.The authorsdemonstratedthemethodonthetransformsoft-norms,t-conorms,uninorms andnullnorms.Oneofthekeystepsofthemethodisfindingabijectivechaincwith respecttoF.Sinceitisnotanobvioustask,itrequiresfurtherresearchefforts. The ninth paper considers the problem of generalizing the Sugeno Integral for AtanassovIntuitionisticFuzzySets.Byconsideringarecentlyintroducedrelation- ship between L-fuzzy measures, integrals and isotone concept-forming operators on a Girard monoid, the generalized notion of Sugeno integral for Atanassov’s intuitionisticL-fuzzysetsisintroduced. Thetenthpapertacklestheproblemofcleanenergymanagementasefficientlyas possible.Makinguseofnaturallanguagetorepresentdifferentparameters,aswellas fuzzylogicmethods,theauthorsproposeanintelligentenergymanagementsystem that can be used in civil and commercial buildings. This proposed system allows selectingthebestenergyfromdifferentavailableenergies,inordertofindthemost economicalwaytofeedtheelectricalconsumption. Intheeleventhpaper,theauthorspresenttheresultsoftheirexperimentsonsolving the so-called Cumulative Capacitated Vehicle Routing Problem. Vehicle Routing Problemsformalargeclassofappliedoptimizationproblems,wherethegoalisto findoptimalroutesformultiplevehiclesvisitingasetoflocations.Thegoalofthe CumulativeCapacitatedVehicleRoutingProblemistominimizethesumofarrival times at customers, but with the constraint of limited capacity. The authors apply theDiscreteBacterialMemeticEvolutionaryAlgorithm(DBMEA),whichwasvery successfulinsolvingotherroutingproblemsintheirpreviousworks.Accordingto theresults,althoughDBMEAcanfindtheoptimalsolutionforsmallinstances,itfails tofindtheoptimuminothercases.Theauthorssuggestsomepossiblemodifications toimprovetheperformanceofthealgorithm. The twelfth paper introduces a new aggregation operator for fuzzy signatures. Fuzzy signatures are nested vector-valued fuzzy sets that can be represented by a tree structure. The aggregation operators applied at the branches are mostly some kindofaveragingoperators,buttherearerealpracticalapplications,whentheyare notabletorepresentthehumanexpert’sknowledge.Toovercomethisshortcoming, the authors introduce a novel aggregation operator on the first level of the fuzzy signature, which is similar to a rule-based inference (Fuzzy Inference System-like Aggregation Operator, FISAO). The practical usefulness is demonstrated on the problemofstructureconditionqualificationofresidentialbuildings. viii Preface Thethirteenthpaperaddressestheproblemofdefiningaclosuresysteminfuzzy latticeswhichmaynothaveapowersetstructure.Oncethedefinitionoffuzzyclosure systemisfixed,theclosureoperatorstructureisextendedandthepropertiesoffuzzy closurerelationsandtheirrelationshipwithfuzzyclosuresystemsarestudied. Thefourteenthpaperstudiestheuseoflocalcongruencestoreduceconceptlattices inFormalConceptAnalysis.Inparticular,theauthorsanalysethemodificationsthat mustbecarriedoutinareducedformalcontextinordertoobtainaconceptlattice isomorphictotheoneprovidedbythereductionofalocalcongruence. Thefifteenthpaperstudiestheconnectionsbetweentwomathematicaltoolswhich weredevelopedinordertomanagetheinformationcollectedindatabases.Inpartic- ular,theauthorsmakeaninitialcomparisonofone-sidedconceptlatticeframework, and several other fuzzy rough set theory and formal concept analysis frameworks. The further development of this study will allow to provide the translation of the resultsgiveninformalconceptanalysisandroughsettheorytotheone-sideconcept lattice. The sixteenth paper addresses the problem of manifold learning, establishing a connection between spaces with a fuzzy partition and Riemannian manifolds. In particular,itisproventhataspacewhosetopologicalstructureischaracterizedby afuzzypartition,naturallyleadstoso-calledRiemannianspacesormanifolds.The importanceofthisfactliesinthemethodsusedbythemachinelearningframework basedonlearningvariousmanifoldsfromdata. Discretefuzzyintegralsarewidelyusedinmulticriteriadecisionsupport,fuzzy rule-based systems, image processing and classification problems, among others. Theseventeenthcontributionproposesanew,generalapproachtotheconstructionof discretefuzzyintegrals.Themethodisbasedonthedecompositionofhypergraphsof survivalfunctionsandonrectanglemappingsevaluatingrectanglesoftheconsidered decompositionsinanon-standardway.Theauthorsillustratetheproposedmethod withseveraldetailedexamples. Theeighteenthpaperinvestigatesthemechanicalbehaviourofmaterials.Within theviscoelasticitytheory,theviscoelasticmaterialsrepresentedbytheirmodelsare studied. The authors assign a V-membership function quantifying the measure of viscous behaviour of the material represented by the model. Consequently, each viscoelastic model can be regarded from the fuzzy viewpoint and the isothermal stateisstudied. Theauthorsofthenineteenthpaperworkonthedetectionoffalsedrivinglicenses. Basedonananalysisofthetwoserialcodesusuallyincludedinlicensesissuedin Europeancountries,theauthorsdevelopamechanismtodetectforgeriesofdriving licenses.Themechanismproposedinthisworkcouldbecombinedwithotherexisting mechanisms,suchasimageanalysisoralgorithmsthatcalculatecheckdigitstoobtain betterresultsinthefieldoffrauddetection. The twentieth paper is devoted to the automatic driver identification by using a procedure based on formal concept analysis. Considering a particular dataset and analysingthevaluesofasubsetofvariablesrelatedtodrivingstyle,attributeimpli- cations are computed and their main features are studied to give support to this procedure. Preface ix Thetwenty-firstpaperproposestheuseofanon-parametricprobabilitydensity estimation method in order to analyse and identify forensic events. A particular dataset containing information about criminal incidents in the city of Baltimore, Maryland,USA,isconsidered.Afterinformationprocessing,analgorithmofkernel estimatorsusingtheeffectiveEpanechnikovfunctionisapplied.Thisresearchallows tolocateareasonthecitymapwherethehighestprobabilityofparticularcrimesare determined. The twenty-second paper develops a model based on fuzzy signatures for its applicationinmaterialhandlingmanagement.Theproposedmodelusessignificantly lessinputparametersthanAhmed’smethodandismoresimpleitselfsinceitisbased on fuzzy signatures instead of fuzzy inferences rules. The approach comes from a real industrial problem, to which the knowledge was given by the experts of the companywheretheexaminationswerecarriedout. The twenty-third paper considers integral aggregation operators with a fuzzy measureinitscoreinordertoprovideatoolforrankingforensicsdataset.Specifically, amethodologybasedontheChoquetintegralisdevelopedforextractinginformation andrankingsuspiciousordifferentdata.Theproposedmethodologyisappliedtoa particularcrimedatasetcorrespondingtophysicaland/orpsychicalgenderviolence. The last paper assesses the effects of knowledge extraction approaches on the cryptanalysisprocess.Theobtainedresultsrevealthattheapproachesinthefieldof knowledgeextractionshouldbehandledmorecomprehensivelyinthecryptanalysis processes, and new assessment criteria should be studied for chaos-based design studies. PuertoReal,Spain MaríaEugeniaCornejo Gyo˝r,Hungary IstvánA.Harmati Gyo˝r,Hungary LászlóT.Kóczy Cádiz,Spain JesúsMedina-Moreno