Partial Order Concepts in Applied Sciences PDF
Preview Partial Order Concepts in Applied Sciences
Marco Fattore · Rainer Bruggemann Editors Partial Order Concepts in Applied Sciences Partial Order Concepts in Applied Sciences Marco Fattore • Rainer Bruggemann Editors Partial Order Concepts in Applied Sciences 123 Editors MarcoFattore RainerBruggemann DepartmentofStatisticsandQuantitative Leibniz—InstituteofFreshwaterEcology Methods andInlandFisheries UniversityofMilan“Milano-Bicocca” Berlin,Germany Milan,Italy ISBN978-3-319-45419-1 ISBN978-3-319-45421-4 (eBook) DOI10.1007/978-3-319-45421-4 LibraryofCongressControlNumber:2016955833 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface On 9th and 10th April 2015, the 11th International workshop on partial orders in applied sciences was held in Florence, Italy. Scientists from several countries gatheredontheTuscanianhillstoshareanddiscussideasonPartialOrderTheory and its applications to open problems in different research fields. This book is the synthesisofwhathasbeenpresentedattheworkshop.Itcollectspapersofdifferent nature (theoretical, applied, computational), pertaining to many different topics, fromindicatorconstructionandclusteranalysisonmulti-indicatorsystemstosocio- economic,environmental,andgeneticapplications. The theory of partially ordered sets (posets, for short) is a well-established and developed branch of discrete mathematics. Differently from classical analysis and linear algebra, it is not part of the standard toolbox of statisticians and applied scientistsyet.However,inthelast15years,interestinapplicationsofposettoolsto differentresearchareashasbeenincreasing.Thereasonsforthatarequiteclear.The descriptionoftheworldaroundusinvolvesincreasinglycomplexmultidimensional data structures, made up of weakly interdependent variables, often of an ordinal kind. Main examples can be found in the socio-economic analysis of well-being orinmanymulti-criteriadecisionproblemsintheenvironmentalsciences.Usually, onewantstoreducecomplexity,makingsyntheticinformationemergeintheform ofindicatorsorofrankingsofstatisticalunits.Theuseofanalyticaltoolsdesigned for highly correlated numerical variables (as in classical dimensionality reduction procedures) is well at odds with synthesizing this kind of data systems. It is the existence of essential (i.e., not due to noise in the data) incomparabilities among statisticalunitstobeofcentralimportance.Incomparabilitiesareanintrinsicfeature of complex data and methods to deal with them are to be worked out, in order to develop data treatment tools capable of simplifying complexity, while preserving itsfundamentalandmeaningfulfeatures.Partialordertheoryisdesignedprecisely to deal with this kind of problems, being a mathematical theory solely based on algebraicrelations,i.e.,hereontheconceptsofcomparabilityandincomparability among “entities” (statistical units, multidimensional profiles:::). The description of complex concepts in several different research fields imports notions and tools fromposettheoryintothedailypracticeofappliedscholars.Thetheoryofpartially v vi Preface ordered sets, however, is not only a way to enlarge the analytical toolbox of data analysts; primarily, it is a way to conceptualize the problems and address them consistently with their nature. From this point of view, the effort of spreading “poset language” across disciplines has also a cultural and epistemological goal, as a contribution towards the development of new paradigms in data analysis and interpretation. Perhaps, this is the most challenging, and the hardest, issue, i.e., to introducethescientificcommunitytoanewlookonnew(andold)problems. Theseriesofpartialorderworkshopsisanattemptinthisperspective,asarethe research results “condensed” in the book. It is a pleasure to see how new results and new applications of the posetic language are continuously worked out, and how poset theory is reaching new scientific areas, as witnessed by the contents of this volume, which cover an astonishing variety of methods and topics. The bookisorganizedintofiveparts.PartIisdevotedtomethodologicaladvancesand collects papers of a more theoretical or technical nature, oriented to the analysis of multi-indicator systems. Part II pertains to applications of poset theory and posetic techniques to socio-economic analysis; multidimensional poverty, social participation, and development are the main topics. In Part III, poset theory is applied to environmental sciences, namely to biodiversity, sustainability, and risk management in the chemical industry. Part IV investigates the use of posetic tools in new application fields, like genetics, botanics, and engineering. Finally, part V presentssomerecentdevelopmentsinsoftwaretoolsforposeticanalysis. Thebookisofinterestbothforscholarsworkingonthespecifictopicstouched uponinthevolumeandforallwhowantstobegentlyintroduced,byexamples,to newideasandperspectivesincomplexdataanalysis.Wehopeitmayinspireother scholars to undertake and tread innovative research paths in their own application fields. Milan,Italy MarcoFattore Berlin,Germany RainerBruggemann Contents PartI TheoreticalandMethodologicalAdvances EndowingPosetswithFlesh:If,WhyandHow? ............................. 3 JanW.Owsin´ski Incomparability/InequalityMeasuresandClustering....................... 21 Hans-GeorgBartelandHans-JoachimMucha Incomparable:WhatNow,IV.Incomparabilities:AModeling Challenge.......................................................................... 35 RainerBruggemann,LarsCarlsen,andPaolaAnnoni PartialOrderingandMetrologyAnalyzingAnalyticalPerformance...... 49 LarsCarlsenandRainerBruggemann FunctionalsandSyntheticIndicatorsOverFinitePosets.................... 71 MarcoFattore Evaluation,ConsideredasProblemOrientableMathematics OverLattices ..................................................................... 87 AdalbertKerber A Combined Lexicographic Average Rank Approach for EvaluatingUncertainMulti-indicatorMatriceswithRiskMetrics........ 105 ElvisHernández-Perdomo,JohnathanMun,andClaudioM.Rocco PartII PartialOrderTheoryinSocio-economicSciences PeculiaritiesinMultidimensionalRegionalPoverty ......................... 121 PaolaAnnoni,RainerBruggemann,andLarsCarlsen Application of Partial Order Theory to Multidimensional PovertyAnalysisinSwitzerland................................................ 135 TugceBeycanandChristianSuter vii viii Contents AnalysisofSocialParticipation:AMultidimensionalApproach BasedontheTheoryofPartialOrdering...................................... 151 StefaniaDellaQueva POSETAnalysisofPanelDatawithPOSAC ................................. 161 Enricodi Bella,MatteoCorsi,andLuciaLeporatti PartiallyOrderedSetTheoryandSen’sCapabilityApproach: AFruitfulRelationship.......................................................... 177 GiulioGuarini PartIII PartialOrderTheoryinEnvironmentalSciences RankingChemicalswithRespecttoAccidentsFrequency.................. 193 GhanimaAl-Sharrah FormalConceptAnalysisApplicationsinChemistry:From RadionuclidesandMolecularStructuretoToxicityandDiagnosis ........ 207 NancyY.QuinteroandGuillermoRestrepo Partial Order Analysis of the Government Dependence oftheSustainableDevelopmentPerformanceinGermany’s FederalStates..................................................................... 219 Alexander Hilckmann, Vanessa Bach, Rainer Bruggemann, RobertAckermann,andMatthiasFinkbeiner PartIV NewApplicationsofPartialOrderTheory AMatchingProblem,PartialOrder,andanAnalysisApplying theCopelandIndex .............................................................. 231 Rainer Bruggemann, Peter Koppatz, Frauke Fuhrmann, andMargitScholl ApplicationoftheMixingPartialOrdertoGenes ........................... 239 William Seitz, Krunoslav Brcˇic´-Kostic´, Petar T. Mitrikeski, andPatriciaSeitz AnalyzingEthnopharmacologicalDataMatricesonTraditional Uses of Medicinal Plants with the Contribution of Partial OrderTechniques................................................................ 251 Stergios Pirintsos, Michael Bariotakis, Danae Laina, ChristosLionis,EliasCastanas,andRainerBruggemann PartV SoftwareDevelopments PARSEC:AnRPackageforPartialOrdersinSocio-Economics .......... 275 AlbertoArcagni »PyHasse«andCloudComputing.............................................. 291 PeterKoppatzandRainerBruggemann Index............................................................................... 301 Contributors RobertAckermann TechnischeUniversitätBerlin,Berlin,Germany Ghanima Al-Sharrah Department of Chemical Engineering, Kuwait University, Safat,Kuwait Paola Annoni Economic Analysis Unit, European Commission-Directorate GeneralforRegionalandUrbanPolicy,Brussels,Belgium AlbertoArcagni DepartmentofStatisticsandQuantitativeMethods,Universityof Milano-Bicocca,Milan,Italy VanessaBach TechnischeUniversitätBerlin,Berlin,Germany Michael Bariotakis Department of Biology, University of Crete, Heraklion, Greece Hans-Georg Bartel Department of Chemistry, Humboldt University Berlin, Berlin,Germany Tugce Beycan Department of Sociology, University of Neuchâtel, Neuchâtel, Switzerland KrunoslavBrcˇic´-Kostic´ InstituteRud¯erBoškovic´,Zagreb,Croatia Rainer Bruggemann Department of Ecohydrology, Leibniz—Institute of Fresh- waterEcologyandInlandFisheries,Berlin,Germany LarsCarlsen AwarenessCenter,Roskilde,Denmark Elias Castanas Laboratory of Experimental Endocrinology, School of Medicine, UniversityofCrete,Heraklion,Greece Matteo Corsi Department of Economics and Business Studies, University of Genoa,Genoa,Italy Stefania DellaQueva ISTAT—ItalianNationalInstituteofStatistics,Rome,Italy ix x Contributors Enrico di Bella Department of Economics and Business Studies, University of Genoa,Genoa,Italy Marco Fattore Department of Statistics and Quantitative Methods, University of Milano-Bicocca,Milan,Italy MatthiasFinkbeiner TechnischeUniversitätBerlin,Berlin,Germany Frauke Fuhrmann Technical University of Applied Sciences Wildau, Wildau, Germany GiulioGuarini DipartimentodiEconomiaeimpresa,Universitàdeglistudidella Tuscia,Viterbo,Italy ElvisHernández-Perdomo UniversityofHull,Hull,UK AlexanderHilckmann TechnischeUniversitätBerlin,Berlin,Germany AdalbertKerber DepartmentofMathematics,UniversityofBayreuth,Bayreuth, Germany PeterKoppatz SudileGbr,Potsdam,Germany TechnicalUniversityofAppliedSciencesWildau,Wildau,Germany DanaeLaina DepartmentofBiology,UniversityofCrete,Heraklion,Greece Lucia Leporatti Department of Economics and Business Studies, University of Genoa,Genoa,Italy Christos Lionis Clinic of Social and Family Medicine, School of Medicine, UniversityofCrete,Heraklion,Greece Petar T. Mitrikeski Institute Rud¯er Boškovic´ & Institute for Research and DevelopmentofSustainableEcosystems,Zagreb,Croatia Hans-JoachimMucha WeierstrassInstituteofAppliedAnalysisandStochastics, Berlin,Germany JohnathanMun U.S.NavalPostgraduateSchool,Monterey,CA,USA Jan W. Owsin´ski Systems Research Institute, Polish Academy of Science, Warszawa,Poland StergiosPirintsos DepartmentofBiology,UniversityofCrete,Heraklion,Greece BotanicalGarden,UniversityofCrete,Rethymnon,Greece Nancy Y. Quintero Laboratorio de Química Teórica, Universidad de Pamplona, Pamplona,Colombia UniversidaddeAntioquia,Antioquia,Colombia UniversidadPontificiaBolivariana,Antioquia,Colombia UniversidadCatólicadeOriente,Antioquia,Colombia
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