Table Of ContentAdvances in Intelligent Systems and Computing 315
Przemysław Grzegorzewski
Marek Gagolewski
Olgierd Hryniewicz
María Ángeles Gil Editors
Strengthening Links
between Data Analysis
and Soft Computing
Advances in Intelligent Systems and Computing
Volume 315
Serieseditor
JanuszKacprzyk,PolishAcademyofSciences,Warsaw,Poland
e-mail:[email protected]
AboutthisSeries
The series “Advances in Intelligent Systems and Computing” contains publications on theory,
applications,anddesignmethodsofIntelligentSystemsandIntelligentComputing.Virtuallyall
disciplinessuch asengineering, natural sciences, computer and informationscience, ICT,eco-
nomics,business,e-commerce,environment,healthcare,lifesciencearecovered.Thelistoftop-
icsspansalltheareasofmodernintelligentsystemsandcomputing.
The publications within “Advances in Intelligent Systems and Computing” are primarily
textbooksandproceedingsofimportantconferences,symposiaandcongresses.Theycoversig-
nificant recent developments in the field, both of a foundational and applicable character. An
importantcharacteristicfeatureoftheseriesistheshortpublicationtimeandworld-widedistri-
bution.Thispermitsarapidandbroaddisseminationofresearchresults.
AdvisoryBoard
Chairman
NikhilR.Pal,IndianStatisticalInstitute,Kolkata,India
e-mail:[email protected]
Members
RafaelBello,UniversidadCentral“MartaAbreu”deLasVillas,SantaClara,Cuba
e-mail:[email protected]
EmilioS.Corchado,UniversityofSalamanca,Salamanca,Spain
e-mail:[email protected]
HaniHagras,UniversityofEssex,Colchester,UK
e-mail:[email protected]
LászlóT.Kóczy,SzéchenyiIstvánUniversity,Gyo˝r,Hungary
e-mail:[email protected]
VladikKreinovich,UniversityofTexasatElPaso,ElPaso,USA
e-mail:[email protected]
Chin-TengLin,NationalChiaoTungUniversity,Hsinchu,Taiwan
e-mail:[email protected]
JieLu,UniversityofTechnology,Sydney,Australia
e-mail:[email protected]
PatriciaMelin,TijuanaInstituteofTechnology,Tijuana,Mexico
e-mail:[email protected]
NadiaNedjah,StateUniversityofRiodeJaneiro,RiodeJaneiro,Brazil
e-mail:[email protected]
NgocThanhNguyen,WroclawUniversityofTechnology,Wroclaw,Poland
e-mail:[email protected]
JunWang,TheChineseUniversityofHongKong,Shatin,HongKong
e-mail:[email protected]
Moreinformationaboutthisseriesathttp://www.springer.com/series/11156
·
Przemysław Grzegorzewski Marek Gagolewski
·
Olgierd Hryniewicz María Ángeles Gil
Editors
Strengthening Links
between Data Analysis
and Soft Computing
ABC
Editors
PrzemysławGrzegorzewski OlgierdHryniewicz
PolishAcademyofSciences PolishAcademyofSciences
SystemsResearchInstitute SystemsResearchInstitute
ul.Newelska6,01-447Warsaw,Poland Warsaw
Poland
and
MaríaÁngelesGil
FacultyofMathematicsand
DepartamentodeEstadistica
InformationSciences
UniversidaddeOviedo
WarsawUniversityofTechnology
Oviedo
ul.Koszykowa75,01-661Warsaw,Poland
Spain
MarekGagolewski
PolishAcademyofSciences
SystemsResearchInstitute
ul.Newelska6,01-447Warsaw,Poland
and
FacultyofMathematicsand
InformationSciences
WarsawUniversityofTechnology
ul.Koszykowa75,01-661Warsaw,Poland
ISSN2194-5357 ISSN2194-5365 (electronic)
ISBN978-3-319-10764-6 ISBN978-3-319-10765-3 (eBook)
DOI10.1007/978-3-319-10765-3
LibraryofCongressControlNumber:2014948458
SpringerChamHeidelbergNewYorkDordrechtLondon
(cid:2)c SpringerInternationalPublishingSwitzerland2015
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe
materialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broad-
casting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformationstorage
andretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknown
orhereafterdeveloped.Exemptedfromthislegalreservationarebriefexcerptsinconnectionwithreviews
orscholarly analysis ormaterial suppliedspecifically forthepurposeofbeingentered andexecuted ona
computersystem,forexclusive usebythepurchaser ofthework.Duplication ofthis publication orparts
thereofispermittedonlyundertheprovisionsoftheCopyrightLawofthePublisher’slocation,initscur-
rentversion,andpermissionforusemustalways beobtained fromSpringer. Permissionsforusemaybe
obtainedthroughRightsLinkattheCopyrightClearanceCenter.Violationsareliabletoprosecutionunder
therespectiveCopyrightLaw.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Whiletheadviceandinformationinthisbookarebelievedtobetrueandaccurateatthedateofpublication,
neither the authors northe editors nor the publisher can accept any legal responsibility for any errors or
omissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,withrespecttothematerial
containedherein.
Printedonacid-freepaper
SpringerispartofSpringerScience+BusinessMedia(www.springer.com)
Preface
Probabilityandstatisticsweretheonlywell-foundedtheoriesofuncertaintyforalong
time.However,duringlastfortyyears,in suchareaslike decisiontheory,artificialin-
telligenceorinformationprocessing,numerousapproachesextendingororthogonalto
the existing theory of probability and mathematical statistics have been successfully
developed.Thesenewapproacheshaveappeared,eitherontheirownlikefuzzysetthe-
ory,possibilitytheory,roughsets,orhavingtheirorigininprobabilitytheoryitself,like
impreciseprobability,belieffunctions,fuzzyrandomvariables.
The commonfeatureof allthose attemptsis to allow for a more flexiblemodeling
ofimprecision,uncertainty,vaguenessandignorance.Theproposednew methodsare
softer than the traditional theories and techniquesbecause being less rigid they more
easilyadapttotheactualnatureofinformation.
Widerangeofapplicationsstillrevealstheneedforsoftextensionsofclassicalprob-
abilityandstatisticaltools.Forexample,indataanalysisanddataminingitisbecoming
increasingly clear that integrating fuzzy sets and probability can lead to more robust
andinterpretablemodelswhichbettercaptureallkindsoftheinformationcontainedin
data. Also, in science and engineeringthe need to analyze and model the true uncer-
taintyassociatedwithcomplexsystemsrequiresamoresophisticatedrepresentationof
ignorancethanthatprovidedbyuninformativeBayesianpriors.
Several years ago, the need was felt to establish a recurrentforum for exchanging
ofideasanddiscussingnewtrendsthatenlargethestatisticalanduncertaintymodeling
traditions, towards a flexible and more specific handling of incomplete or subjective
information.ThisidearesultedinaseriesofbiannualinternationalconferencesonSoft
MethodsinProbabilityandStatistics(SMPS),organizedforthefirsttimeinWarsaw
in2002.Subsequenteventsin thisseriestookplaceinOviedo(2004),Bristol(2006),
Toulouse(2008),Oviedo/Mieres(2010)andKonstanz(2012).
Thisvolumeisa collectionofpaperspresentedatthe7thInternationalConference
onSoftMethodsinProbabilityandStatistics–SMPS2014,heldinWarsaw(Poland)on
September22–24,2014.TheconferencewasorganizedbythePolishOperationaland
SystemsResearch Society,SystemsResearch Institute of the Polish Academyof Sci-
encesandthe Facultyof MathematicsandInformationScienceofWarsaw University
ofTechnology.
VI Preface
The volume contains three sections. The first one is dedicated to general aspects
of uncertainty modeling and processing – starting from some fundamentalproblems,
throughvarioustoolsandapproachesincludingBayesiananalysis,fuzzysetsandtheir
generalizations, fuzzy equations etc. Part two encloses contributions devoted to soft
methods in statistics emphasizing robust analysis and hypotheses testing in the pres-
ence of imprecise data. Part three consists of papersorientedon soft methodsin data
analysis.Herewefindcontributionsconcentratedonstatisticalmethodsindatamining,
likewise combing statistical and soft computing perspectives – both more theoretical
andorientedonapplications.
Theeditorsaregratefultocontributingauthors,invitedspeakers,ProgramCommit-
teemembersandadditionalrefereeswhomadeitpossibletoputtogethertheattractive
programoftheconference.WethanktheeditoroftheSpringerseriesAdvancesinSoft
Computing,prof.JanuszKacprzyk,andSpringer-Verlagforthededicationtothepro-
ductionofthisvolume.
Warsaw,June23,2014 PrzemysławGrzegorzewski
MarekGagolewski
OlgierdHryniewicz
MaríaÁngelesGil
Organization
Executive Board
MaríaÁngelesGil(Oviedo,Spain)
PrzemysławGrzegorzewski(Warsaw,Poland)
OlgierdHryniewicz(Warsaw,Poland)
Program Committee
BernarddeBaets(Gent,Belgium)
ChristianBorgelt(Mieres,Spain)
GiulianellaColetti(Perugia,Italy)
AnaColubi(Oviedo,Spain)
InesCouso(Oviedo,Spain)
DidierDubois(Toulouse,France)
FabrizioDurante(Bolzano,Italy)
PierpaoloD’urso(Roma,Italy)
MaríaÁngelesGil(Oviedo,Spain)
GilGonzálezRodríguez(Oviedo,Spain)
PrzemysławGrzegorzewski(Warsaw,Poland)
OlgierdHryniewicz(Warsaw,Poland)
EykeHüllermeier(Marburg,Germany)
PiotrJaworski(Warsaw,Poland)
JanuszKacprzyk(Warsaw,Poland)
FrankKlawonn(Braunschweig/Wolfenbüttel,Germany)
JacekKoronacki(Warsaw,Poland)
RudolfKruse(Magdeburg,Germany)
MarkLast(Negev,Israel)
JonatanLawry(Bristol,UK)
RadkoMesiar(Bratislava,Slovakia)
EnriqueMiranda(Oviedo,Spain)
SusanaMontes(Oviedo,Spain)
VIII Organization
ZbigniewNahorski(Warsaw,Poland)
BeloslavRiecan(BanskáBystrica,Slovakia)
DanielSanchez(Granada,Spain)
MartinStepnicka(Ostrava,CzechRepublic)
SeyedMahmoodTaheri(Isfahan,Iran)
WolfgangTrutschnig(Salzburg,Austria)
StefanVanAelst(Ghent,Belgium)
BarbaraVantaggi(Roma,Italy)
ReinhardViertl(Vienna,Austria)
BerlinWu(Taipei,Taiwan)
Additional Reviewers
Adrian Ban, Humberto Bustince, Lucian Coroianu, Anna Czapkiewicz,
Glad Deschrijver, Maria Brigida Ferraro, Marek Gagolewski, Piotr Nowak, Anna
Olwert,AnnaStachowiak,LucianoStefanini,ValentinTodorov,JinHeeYoon,Jinping
Zhang
OrganizingCommittee
AnnaCena
MarekGagolewski–publicationandconferencewebsitechair
PrzemysławGrzegorzewski–localchair
AdamKołacz
KarolOpara
BarbaraZ˙ogała-Siudem
Contents
PartI:SoftMethods inUncertainty Modeling andProcessing
ModelsandDecisions
DecidingunderIgnorance:InSearchofMeaningfulExtensionsofthe
HurwiczCriteriontoDecisionTrees.................................. 3
DidierDubois,HélèneFargier,RomainGuillaume,CarolineThierry
ComparisonofFuzzyandCrispRandomVariablesbyMonte Carlo
Simulations ...................................................... 13
OlgierdHryniewicz
StochasticOrdersforFuzzyRandomVariables ........................ 21
IgnacioMontes,EnriqueMiranda,SusanaMontes
IntervalCompositionalData:ProblemsandPossibilities................. 29
OndrˇejPavlacˇka,KarelHron
Interval-ValuedandIFSets
ANewDefinitionofEvaluation/DefuzzificationofanIntervalType-2
FuzzySet ........................................................ 37
LucaAnzilli,GisellaFacchinetti,TommasoPirotti
ConnectingInterval-ValuedFuzzySetswithImpreciseProbabilities....... 47
IgnacioMontes,EnriqueMiranda,SusanaMontes
OnIncompleteLabelRankingwithIF-sets ............................ 55
PawełP.Ładyz˙yn´ski,PrzemysławGrzegorzewski
OntheContinuityofProbabilityonIFSets ........................... 63
BeloslavRiecˇan,AlžbetaMichalíková
