Studies in Computational Intelligence 819 László T. Kóczy Jesús  Medina-Moreno Eloísa Ramírez-Poussa Alexander Šostak    Editors Computational Intelligence and Mathematics for Tackling Complex Problems Studies in Computational Intelligence Volume 819 Series Editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland The series “Studies in Computational Intelligence” (SCI) publishes new develop- mentsandadvancesinthevariousareasofcomputationalintelligence—quicklyand 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 the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution, which enable both wide and rapid dissemination of research output. The books of this series are submitted to indexing to Web of Science, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink. More information about this series at http://www.springer.com/series/7092 á ó ó ú L szl T. K czy Jes s Medina-Moreno (cid:129) (cid:129) í í Š Elo sa Ram rez-Poussa Alexander ostak (cid:129) Editors Computational Intelligence and Mathematics for Tackling Complex Problems 123 Editors LászlóT. Kóczy Jesús Medina-Moreno Faculty of Engineering Sciences Science Faculty SzéchenyiIstván University Department ofMathematics Gyõr,Hungary University of Cádiz Cádiz,Spain BudapestUniversity of Technology andEconomics Alexander Šostak Budapest, Hungary Institute of Mathematics Eloísa Ramírez-Poussa andComputer Science University of Latvia Faculty of Economic and Riga, Latvia Business Sciences Department ofMathematics Department ofMathematics University of Cádiz University of Latvia Cádiz,Spain Riga, Latvia ISSN 1860-949X ISSN 1860-9503 (electronic) Studies in Computational Intelligence ISBN978-3-030-16023-4 ISBN978-3-030-16024-1 (eBook) https://doi.org/10.1007/978-3-030-16024-1 LibraryofCongressControlNumber:2019934777 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface Advances in Computational Intelligence and Mathematics for Tackling Complex Problems Many areas of modern knowledge encounter problems, whose solution is impos- siblewithoutapplyingadvancedmathematicaltechniquesaswellascomputational intelligence-based methods. Moreover, the interaction and interplay between mathematical techniques and computational technologies are fundamental for the adequate approach of the research of such problems. Among the most important mathematical tools for this interaction are fuzzy logic-based mathematical tech- nologies and rough set-based methodologies. These technologies and specifically theirinterplayallowtoaddressdifferentchallengesofthepresenttechnologicalage. Manyareasofmodernknowledgeencountertheproblemsthesolutionofwhich presupposes the use of both advanced mathematical techniques and computational intelligence-based research methods. In this volume, these two research areas, computational intelligence and math- ematics, are connected in attractive contributions devoted to the solution of some tempting theoretical and real-world important problems. The volume is mainly composed of the extended and reviewed versions of the highest quality papers presented by participants from diverse countries of the world such as Japan, Mexico, Chile and Cuba at the Tenth European Symposium on Computational Intelligence and Mathematics (ESCIM 2018) held in Riga, the capital of Latvia, fromOctober7to10.Besides,thetechnicalprogrammeoftheconferenceincluded four substantial keynote presentations given by Profs. Janusz Kacprzyk from Poland (description of human-centric systems: a crucial role of bipolarity in judgements and intentions), Oscar Castillo from Mexico (nature-inspired opti- mization of type-2 fuzzy logic controllers), Gabriella Pasi, from Italy (aggregation guidedbyfuzzyquantifiersinIRandsocialmediaanalytics)andAlexanderŠostak fromLatvia(onmany-levelfuzzyroughapproximationsystems).Inthesequel,we give a brief summary of the contributions contained in this volume. v vi Preface The first and the twelfth papers, written by a group of Hungarian authors, are devoted to the development offuzzy signature-based models. In the first paper, a new fuzzy signature modelling packaging decision is developed. It is based on logistics expert opinions and aimed to support the decision-making process by choosing the right packaging system specifically aimed for dangerous goods packaging.Initsturn,thetwelfthpaperpresentsanewfuzzysignature-basedmodel forthequalificationofresidentialbuildings.Thismodelisusingastructureoffuzzy signaturewithvariableaggregations,wherethedefinitionofaggregationismadeby parameters and the values of parameters are changing depending on the specific application. The second paper presents a new classifier architecture based on fuzzy finger- print relevance classifier. This classifier is worked out by a group of Portuguese researchers. Specifically, this classifier allows to get good results in the process of automatic identifying patient innovation solutions from texts obtained by means of the Web. Theauthorsofthethirdpaper,researchersfromtheSzechenyiIstvanUniversity in Hungary, propose an interesting population-based memetic algorithm, so-called discrete bacterial memetic evolutionary algorithm, appropriate for solving the one-commodity pickup-and-delivery travelling salesman problem. The algorithm was tested on benchmark instances, and the results were compared with the state-of-the-artmethodsintheliterature,illustratingtheadvantagesoftheproposed algorithm. InthefourthpaperpresentedbyresearchersfromUniversityofDebrecen,some interesting possible connections between concepts of roughness and fuzziness are studied. It is shown that a rough membership function can be interpreted as a special type of a fuzzy membership function. This fact is applied to investigate some interplay between the two theories. Themaingoalofthefifthpaper,writtenbyagroupofHungarianscientists,isto find a method that would allow to indicate some characteristic points that can be used for fitting two measured surfaces together. In order to get such a method, the authorsintroduce fuzzyversionofaHoughtransformthatallowstodetectstraight line segments on the image. As different from the classical Hough transform, its fuzzy version is useful in case when the lines are not precisely given or not pre- ciselystraight.Theauthorsapplythismethodforfindingthesamelocationontwo measured versions of a surface. The authors of the sixth paper analyse the behaviour of the so-called rescaled algorithmforfuzzycognitivemapswithrespecttotheexistenceanduniquenessof fixedpointsofsuchmaps.Thisproblemisimportantfortheuseoffuzzycognitive maps in network-like decision support tools. Intheseventhpaper,theclassofgroup-likeuninormsisintroducedasasubclass of group-like FLe algebras, where the underlying universe is order isomorphic to the real line interval (0,1). The author, from the University of Pécs in Hungary, presents some methods of construction of such uninorms and besides gives a complete characterization of this class in case of uninorms with a finite number of idempotent elements. Preface vii The next paper presents the results of the research work in the field of adjoint triplesdoneintheDepartmentofMathematics,UniversityofCádiz,Spain.Adjoint triples arise as an important generalization of t-norms and corresponding residua- tion, since they provide more flexibility and increase the range of possible appli- cation. The authors analyse how the exchange principle law should be defined on adjointtriplesandwhatconditionstheconjunctionofanadjointtripleshouldfulfil in order to guarantee that the corresponding residuated implications satisfy the prescribed property. Theninthpaperpresentstheresultsoftheresearchdonebymathematiciansfrom Serbia. Basing on the known fact that in every finite poset each element can be presented as a join of completely join-irreducible elements, the authors justify the introductionofanewconceptofaposet-valuedreciprocal(preference)relationsas wellasitsintuitionisticcounterpart.Inthisrepresentation,join-irreducibleelements represent pieces of information that reflect the grade of preference in this framework. In their previous research, the authors of the tenth paper showed that the cate- goryofChucorrespondencesbetweenHilbertcontextsisequivalenttothecategory ofpropositionalsystems(thealgebraiccounterpartofthesetofclosedsubspacesof a Hilbert space). These researchers from Spain and Slovakia extend in the present paper the previously obtained results to the big toy models (in the sense of S. Abramsky) introduced as a tool to represent quantum systems in terms of Chu spaces. Specifically, the authors obtain a categorical equivalence between big toy models and a suitable subcategory of the category of Hilbert formal contexts and Chu correspondences. This result is a new example of interesting structures which are representable in terms of Chu correspondences. InthenextpaperwrittenbyPolishscientists,theauthorscontinuetheirprevious research on attribute selection by Hellwig method in case when the data set is expressed via an Atanassov intuitionistic fuzzy set. The authors present a novel extension of Hellwig method for the reduction of data, which was primarily pro- posed for economic data analysis. In this method, the authors use three-term rep- resentation of fuzzy intuitionistic sets, that is taking into account the degree of membership, non-membership and hesitation. The next two papers are written by scientists from different institutions in Poland. The thirteenth paper is devoted to the day and night design of a fuzzy systemfortheclassificationofbloodpressureload.Theauthorsanalysetheloadof 30patients,whichwereclassifiedbythefuzzyclassifierandindicatedahighindex of people with a pressure load. The executed analysis indicates that for these patients, a cardiovascular event could occur at any time of day and night. The authors of the fourteenth paper develop an example of the application of a flower pollination algorithm for the probabilistic neural network learning process. Special attention authors pay on the investigation of the inertial parameters of this algorithm. In the next paper, written by a group of Japanese scientists and presented by Tsuchiya Takeshi, the authors propose a new search method of various tourist information in one prefecture in Japan. This method is using paragraph vector that viii Preface extracts features by a combination of words and word ordering that is included in the content. The sixteenth paper is presented by a researcher of the Siemens AG, Corporate TechnologyinGermany.Itdealswithtransformutilityvaluestopreferencevalues— the problem actual for decision support and recommender systems. Basing on the Łukasiewicz transitivity, the author derives a new transformation and examines its mathematical properties. Fuzzyrelationalequationsandinequalitiesplayanimportantroleinmanytools offuzzymodellingandhavebeenextensivelystudied.Intheseventeenthpaper,the authors from the University of Latvia present a method allowing to convert a system of fuzzy relational constraints with max-t-norm composition to a linear constraint system by adding integer variables. A numerical example is given to illustrate this method. The eighteenth paper, written by a team composed by researchers from Cuba, Chile and Spain, analyses the main variables—causes and effect—related to the enterprisearchitectureandthemultifactorialelementsimpregnatedwithuncertainty that affects it.The knowledgegiven byexpertsistranslatedintodependence rules, whichalsohavebeenanalysedfromafuzzypointofviewusingthefuzzyrelation equation theory. For the use of time series, it is often crucial to obtain, as much detailed infor- mation as possible, from these series. The team of researchers from the University ofCastilla–LaMancha,fromSpain,presentsinthenineteenthpaperatechniquefor obtaininglinguisticdescriptionfromtimeseriesusingarepresentationcalledfuzzy piecewiselinearsegments.Itisshownhowtoobtaintheinformationofamodelled series using this representation and the necessary steps to generate the description by using templates. The twentieth paper is written by Lithuanian and Hungarian researchers, and it presents a new approach for the evaluation of management questionnaires. It combines expert knowledge about the fuzzy signature structure with the hybrid minimizationofsquarederrorsamongleavesandreconstructedvaluesattheleaves. It is shown that this method is more advanced than the mere use of expert knowledge or expert knowledge enhanced with statistical analysis. Fuzzy partitions in many cases are the core of the first step of fuzzification procedure. They are defined in different ways, but usually by taking into account aspectsofthewholeuniverse.Ontheotherhand,thetwenty-firstpaper,writtenby mathematicians from Malaga University, presents a method to define fuzzy parti- tion for elements in the universe holding certain fuzzy attribute. Specifically, the presented technique for the construction of fuzzy partitions according to a fuzzy context is based on fuzzy transforms. The next two papers are written by Latvian mathematicians. In the twenty-second paper, a special construction of a general aggregation operator is proposed. This construction allows to aggregate fuzzy sets taking into account the distance between elements of the universe. Specifically, the authors describe how thisconstructioncouldbeappliedfortheriskassessmentinthecasewhenastrong fuzzy metric is used to characterize the similarity of objects under evaluation. Preface ix In the twenty-third paper, a many-level approach to fuzzy rough approximation for fuzzy sets is developed. It is based on the many-level rough approximation operators introduced in the paper. Basic properties of such operators are studied. Besides,themeasureofthisapproximationisdefinedandstudied.Thismeasurein some sense describes the quality of the obtained approximation. The last paper in this volume presents the research of mathematicians from University of Cádiz, Spain. Here, the philosophy of rough set theory is applied in order to reduce formal context in the environment of formal concept analysis. Specifically, a reduction mechanism based on the consideration of bireducts is proposed, and some properties of the reduced contexts are studied. Finally,wewouldliketofinishthisprefaceshowingouracknowledgementtothe authors members of the programme committee and reviewers, since without their effort and interest, this special issue would not have been possible. We also acknowledge the support received from the University of Cádiz, the Hungarian Fuzzy Association, the Szechenyi Istvan University, the Institute of Mathematics andCS,UniversityofLatviaandtheStateResearchAgency(AEI)andtheEuropean RegionalDevelopmentFund(FEDER)researchprojectTIN2016-76653-P.Finally, a word of thanks is also due to EasyChair, for the facilities provided in the submission/acceptance of thepapers, and inthe preparation ofthis book. Gyõr/Budapest, Hungary László T. Kóczy Cádiz, Spain Jesús Medina-Moreno Cádiz, Spain Eloísa Ramírez-Poussa Riga, Latvia Alexander Šostak October 2018