Table Of ContentAdvances in Intelligent Systems and Computing 832
Sébastien Destercke
Thierry Denoeux · María Ángeles Gil
Przemyslaw Grzegorzewski
Editors
Olgierd Hryniewicz
Uncertainty
Modelling
in Data
Science
Advances in Intelligent Systems and Computing
Volume 832
Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: [email protected]
The series “Advances in Intelligent Systems and Computing” contains publications on theory,
applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all
disciplines such as engineering, natural sciences, computer and information science, ICT, economics,
business,e-commerce,environment,healthcare,lifesciencearecovered.Thelistoftopicsspansallthe
areasofmodernintelligentsystemsandcomputingsuchas:computationalintelligence,softcomputing
including neural networks, fuzzy systems, evolutionary computing and the fusion of these paradigms,
social intelligence, ambient intelligence, computational neuroscience, artificial life, virtual worlds and
society, cognitive science and systems, Perception and Vision, DNA and immune based systems,
self-organizing and adaptive systems, e-Learning and teaching, human-centered and human-centric
computing,recommendersystems,intelligentcontrol,roboticsandmechatronicsincludinghuman-machine
teaming, knowledge-based paradigms, learning paradigms, machine ethics, intelligent data analysis,
knowledgemanagement,intelligentagents,intelligentdecisionmakingandsupport,intelligentnetwork
security,trustmanagement,interactiveentertainment,Webintelligenceandmultimedia.
Thepublicationswithin“AdvancesinIntelligentSystemsandComputing”areprimarilyproceedings
ofimportantconferences,symposiaandcongresses.Theycoversignificantrecentdevelopmentsinthe
field,bothofafoundationalandapplicablecharacter.Animportantcharacteristicfeatureoftheseriesis
theshortpublicationtimeandworld-widedistribution.Thispermitsarapidandbroaddisseminationof
researchresults.
AdvisoryBoard
Chairman
NikhilR.Pal,IndianStatisticalInstitute,Kolkata,India
e-mail:[email protected]
Members
RafaelBelloPerez,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,Győr,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
é
S bastien Destercke Thierry Denoeux
(cid:129)
í Á
Mar a ngeles Gil Przemyslaw Grzegorzewski
(cid:129)
Olgierd Hryniewicz
Editors
Uncertainty Modelling
in Data Science
123
Editors
Sébastien Destercke Przemyslaw Grzegorzewski
CNRS, Heudiasyc Faculty of Mathematics andInformation
Sorbonne universités,Université Science
detechnologie deCompiègne Warsaw University of Technology
Compiegne, France Warsaw,Poland
Thierry Denoeux and
CNRS, Heudiasyc
Sorbonne universités,Université Systems Research Institute
detechnologie deCompiègne Polish Academy ofSciences
Compiegne, France Warsaw,Poland
MaríaÁngeles Gil OlgierdHryniewicz
Department ofStatistics andOperational Department ofStochastic Methods,
ResearchandMathematics Didactics SystemsResearch Institute
University of Oviedo Polish Academy ofSciences
Oviedo,Asturias Warsaw,Poland
Spain
ISSN 2194-5357 ISSN 2194-5365 (electronic)
Advances in Intelligent Systems andComputing
ISBN978-3-319-97546-7 ISBN978-3-319-97547-4 (eBook)
https://doi.org/10.1007/978-3-319-97547-4
LibraryofCongressControlNumber:2018950094
©SpringerNatureSwitzerlandAG2019
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Preface
This volume contains the peer-reviewed papers presented at the 9th International
Conference on Soft Methods in Probability and Statistics (SMPS 2018), which
was held in conjunction with the 5th International Conference on Belief Functions
(BELIEF 2018) on 17–21 September 2018 in Compiègne, France. The series of
biannual International Conference on Soft Methods in Probability and Statistics
startedinWarsawin2002.ItthensuccessfullytookplaceinOviedo(2004),Bristol
(2006),Toulouse(2008),Oviedo/Mieres(2010),Konstanz (2012), Warsaw (2014)
and Rome (2016). SMPS and BELIEF 2018 were organized by the Heudiasyc
laboratory at the Université de Technologie de Compiègne.
Over the last decades, the interest for extensions and alternatives to probability
and statistics has significantly grown in areas as diverse as reliability,
decision-making,dataminingandmachinelearning,optimization,etc.Thisinterest
comes from the need to enrich existing models, in order to include different facets
of uncertainty such as ignorance, vagueness, randomness, conflict or imprecision.
Frameworks such as rough sets, fuzzy sets, fuzzy random variables, random sets,
belief functions, possibility theory, imprecise probabilities, lower previsions,
desirable gambles all share this goal, but have emerged from different needs. By
putting together the BELIEF and SMPS conferences, we hope to increase the
interactionsanddiscussionsbetweenthetwocommunitiesandtoconvergetowards
a more unified view of uncertainty theories.
We also think that the advances, results and tools presented in this volume are
important in the ubiquitous and fast-growing fields of data science, machine
learning and artificial intelligence. Indeed, an important aspect of some of the
learned predictive models is the trust one places in them. Modelling carefully and
with principled methods, the uncertainty associated to the data and the models is
oneofthemeanstoincreasethistrust,asthemodelwillthenbeabletodistinguish
reliable predictions from less reliable ones. In addition, extensions such as fuzzy
sets can be explicitly designed to provide interpretable predictive models,
facilitating user interaction and increasing their trust.
v
vi Preface
The joint event collected 76 submissions, each reviewed by at least two
reviewers.Twenty-nineoftheseareincludedinthepresentvolume,whichcontains
contributions of foundational, methodological and applied nature, on topics as
varied as imprecise data handling, linguistic summaries, model coherence, impre-
cise Markov chains and robust optimization. The resulting proceedings was easily
produced through the use of EasyChair.
We would like to thank all the persons that made this volume and this confer-
ence possible which include all contributing authors, organizers, programme
committee members that help to build such an attractive programme. We are
especially grateful to our three invited speakers, Thomas Augustin (Ludwig-
Maximilians-UniversitätMünchen)forhistalk“Belieffunctionsandvalidstatistical
inference”, Scott Ferson (University of Liverpool) for his talk “Non-Laplacian
uncertainty:practicalconsequencesofanuglyparadigmshiftabouthowwehandle
not knowing” and Ryan Martin (North Carolina State University) for his talk
“Belief functions and valid statistical inference”. We would like to thank all our
generous sponsors: Elsevier and the International Journal of Approximate
Reasoning, the Laboratory of excellence MS2T, the Heudiasyc laboratory, the
International Society of Information Fusion (ISIF), the Compiègne University of
Technology,thecityofCompiègne.Furthermore,wewouldliketothanktheeditor
oftheSpringerseries ofAdvancesinSoft Computing,Prof. Janusz Kacprzyk, and
Springer-Verlag for their dedication to the production of this volume.
June 2018 Sébastien Destercke
Thierry Denoeux
María Ángeles Gil
Przemyslaw Grzegorzewski
Olgierd Hryniewicz
Organization
Programme Committee
Alessandro Antonucci IDSIA
Thomas Augustin DepartmentofStatistics,Univ.ofMunich(LMU)
Giulianella Coletti University of Perugia
Olivier Colot Université Lille 1
Ana Colubi University of Oviedo
Frank Coolen Department of Mathematical Sciences, Durham
University
Inés Couso University of Oviedo
Fabio Cuzzolin Oxford Brookes University
Fabio D’Andreagiovanni Université de Technologie de Compiègne,
UMR CNRS Heudiasyc
Pierpaolo D’Urso Sapienza University of Rome
Bernard De Baets Ghent University
Thierry Denoeux Université de Technologie de Compiègne,
UMR CNRS Heudiasyc
Sébastien Destercke Université de Technologie de Compiègne,
UMR CNRS Heudiasyc
Jean Dezert Onera
Didier Dubois Université de Paul Sabatier, Toulouse,
UMR IRIT
Fabrizio Durante Università del Salento, Lecce
Zied Elouedi Institut Supérieur de Gestion de Tunis
Ramasso Emmanuel Ecole Nationale Supérieure de Mécanique et des
Microtechniques, FEMTO-ST
Maria Brigida Ferraro Department of Statistical Sciences, Sapienza
University of Rome
Maria Angeles Gil Alvarez University of Oviedo
vii
viii Organization
Lluis Godo Artificial Intelligence Research Institute,
IIIA - CSIC
Gil González-Rodríguez University of Oviedo
Michel Grabisch Université Paris I
Przemyslaw Grzegorzewski Systems Research Institute Polish Academy
of Sciences
Olgierd Hryniewicz Polish Academy of Sciences, Systems Research
Institute
Radim Jirousek University of Economics
Anne-Laure Jousselme NATO Centre for Maritime Research
and Experimentation (CMRE)
Frank Klawonn Ostfalia University of Applied Sciences
Vaclav Kratochvil UTIA
Rudolf Kruse University of Magdeburg
Eric Lefevre LGI2A Université d’Artois
Liping Liu The University of Akron
María Asunción Lubiano Universidad de Oviedo
Arnaud Martin Université de Rennes1/IRISA
Ronald W. J. Meester Vrije Universiteit Amsterdam
David Mercier Université d’Artois
Radko Mesiar Slovak University of Technology Bratislava
Rombaut Michele Gipsa-lab
Daniel Milan Institute of Computer Science,
The Czech Academy of Sciences
Enrique Miranda University of Oviedo
Ignacio Montes Carlos III University of Madrid
Susana Montes University of Oviedo
Serafin Moral University of Granada
Frédéric Pichon Université d’Artois
Benjamin Quost Université de Technologie de Compiègne,
UMR CNRS Heudiasyc
Ana Belén Ramos Guajardo University of Oviedo
Johan Schubert Swedish Defence Research Agency
Ferson Scott University of Liverpool, Institute for Risk
and Uncertainty
Prakash P. Shenoy University of Kansas School of Business
Beatriz Sinova University of Oviedo
Martin Stepnicka IRAFM, University of Ostrava
Barbara Vantaggi Sapienza University of Rome
Jirina Vejnarova Institute of Information Theory and Automation
of the AS CR
Paolo Vicig University of Trieste
Liu Zhunga Northwestern Polytechnical University
Contents
Imprecise Statistical Inference for Accelerated Life Testing Data:
Imprecision Related to Log-Rank Test. . . . . . . . . . . . . . . . . . . . . . . . . . 1
Abdullah A. H. Ahmadini and Frank P. A. Coolen
Descriptive Comparison of the Rating Scales Through Different Scale
Estimates: Simulation-Based Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 9
Irene Arellano, Beatriz Sinova, Sara de la Rosa de Sáa,
María Asunción Lubiano, and María Ángeles Gil
Central Moments of a Fuzzy Random Variable Using the Signed
Distance: A Look Towards the Variance . . . . . . . . . . . . . . . . . . . . . . . . 17
Rédina Berkachy and Laurent Donzé
On Missing Membership Degrees: Modelling Non-existence,
Ignorance and Inconsistency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Michal Burda, Petra Murinová, and Viktor Pavliska
Characterization of Conditional Submodular Capacities:
Coherence and Extension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Giulianella Coletti, Davide Petturiti, and Barbara Vantaggi
Some Partial Order Relations on a Set of Random Variables . . . . . . . . 42
Bernard De Baets and Hans De Meyer
A Desirability-Based Axiomatisation for Coherent Choice Functions. . . 46
Jasper De Bock and Gert de Cooman
Cycle-Free Cuts of the Reciprocal Relation Generated by Random
Variables that are Pairwisely Coupled by a Frank Copula . . . . . . . . . . 54
Hans De Meyer and Bernard De Baets
Density Estimation with Imprecise Kernels:
Application to Classification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Guillaume Dendievel, Sebastien Destercke, and Pierre Wachalski
ix
