Table Of ContentStudies 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,
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ThisseriesalsopublishesOpenAccessbooks.ArecentexampleisthebookSwan,
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· ·
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)
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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
