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  • Studies in Fuzziness and Soft Computing 298

    Editor-in-ChiefProf. Janusz KacprzykSystems Research InstitutePolish Academy of Sciencesul. Newelska 601-447 WarsawPolandE-mail: kacprzyk@ibspan.waw.pl

    For further volumes:http://www.springer.com/series/2941

  • Rudolf Seising, Enric Trillas, Claudio Moraga,and Settimo Termini (Eds.)

    On Fuzziness

    A Homage to Lotfi A. Zadeh Volume 1


  • EditorsDr. Rudolf SeisingEuropean Centre for Soft ComputingEdificio de Investigacin, 3a Planta.MieresAsturiasSpain

    Prof. Enric TrillasEuropean Centre for Soft ComputingEdificio de Investigacin, 3a Planta.MieresAsturiasSpain

    Prof. Claudio MoragaEuropean Centre for Soft ComputingEdificio de Investigacin, 3a Planta.MieresAsturiasSpain

    Prof. Settimo TerminiDepartment of Mathematics and InformaticsUniversit di PalermoPalermoItaly

    ISSN 1434-9922 e-ISSN 1860-0808ISBN 978-3-642-35640-7 e-ISBN 978-3-642-35641-4DOI 10.1007/978-3-642-35641-4Springer Heidelberg New York Dordrecht London

    Library of Congress Control Number: 2012954156

    c Springer-Verlag Berlin Heidelberg 2013This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe 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 or informationstorage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodologynow known or hereafter developed. Exempted from this legal reservation are brief excerpts in connectionwith reviews or scholarly analysis or material supplied specifically for the purpose of being enteredand executed on a computer system, for exclusive use by the purchaser of the work. Duplication ofthis publication or parts thereof is permitted only under the provisions of the Copyright Law of thePublishers location, in its current version, and permission for use must always be obtained from Springer.Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violationsare liable to prosecution under the respective Copyright Law.The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoes not imply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.While the advice and information in this book are believed to be true and accurate at the date of pub-lication, neither the authors nor the editors nor the publisher can accept any legal responsibility for anyerrors or omissions that may be made. The publisher makes no warranty, express or implied, with respectto the material contained herein.

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  • Lotfi Zadeh and three unknown persons in the 1950s as an instructorat Columbia University in New York.

  • A Foreword

    When I started looking at the material in this awesome volume, the first thoughtthat came to mind was social network. While this term has been greatly overusednowadays by the media, this volume is clearly a social network with Lotfi Zadeh atthe center. The term is even more appropriate in the case of Zadeh, who in addition tobeing a thinker of historical note, is an extremely social human being. In addition toproviding inspiring technical ideas that have allowed many people in this network tocarve out impressive careers of their own, Lotfi has often provided advice on mattersboth professional and personal to members of this network. Lotfi was never too busyto listen to the problems of others. I often observed that Lotfi had more patiencelistening to others social problems than technical matters. These pieces help toprovide views of Zadeh as if looking into a big house through different windows.

    This volume, in addition to providing insights to the individual contributors ex-periences with Lotfi either socially or technically, even more interestingly it providesthe opportunity to experience in many cases, another dimension of the contributors.While I have known most of the contributors to this volume for many years, this isone of few, if not only occasion, I have had to read their writings on a non-technicaland more personal subject. In many cases, I found this to be a rewarding and an eyeopening experience as I am sure other readers of this book will find.

    The inclusion of pictures tremendously enhances the pleasure of this volume. Notonly are there pictures of Lotfi but enjoyable pictures of other members of the com-munity. The pictures in this volume almost span the life of the idea of fuzziness.They include black and white pictures vintage pictures from the pre-digital days thatare almost invaluable. These pictures inspire warm memories. For me, it was quitenotable to observe the consistency of Lotfis physical appearance over the long his-tory that these pictures cover.

    Lotfi spent many years on the outside trying to convince people of the value of hisidea of fuzzy sets before the successful applications in Japan showed its usefulness.It is worth noting that these pioneering applications in Japan occurred at a time whenJapan was a rapidly raising star in the worlds technological and economic order; afact that amplified and accelerated the worlds appreciation for fuzzy sets. In manyways Lotfi is still an outsider, in this case in his own fuzzy set community. Mostof the applications of fuzzy sets are based on the Mamdani-Sugeno model. Thisparadigm is a kind of disjunctive approach, as we get more information we addpossibilities. Zadehs perspective, as conveyed with his paradigm of restriction-basedsemantics, is a kind of conjunctive approach, as we get more information we reducepossibilities.

  • VIII Foreword by Ronald R. Yager

    Even now as he marches into his nineties and is unable to attend conferencesand interact with fellow attendees as he so enjoys, Lotfi continues to build a socialnetwork. This time using the latest technology, the Internet, he has built a socialnetwork around his inspired idea of the Berkeley Initiative in Soft Computing. Everyday I receive messages from people around the world via this network of interrelatedscholars. These messages usually involve interesting ideas rather then simply beingannouncements of conferences as is the case with some other groups. The mostinteresting and challenging are those that come from Lotfi, particularly those relatedto his attempt to deal with the issue of causality.

    The editors Rudolf Seising, Enric Trillas, Claudio Moraga and Settimo Terminiare to be congratulated for coming up with such a wonderful idea to help celebrate alife as rich and human as Zadehs in this manner.

    Ronald R. YagerNew York City, July, 2012

    Fig. 0.1. Ron R. Yager lecturing at the 14th International Conference on Information Process-ing and Management of Ucertainty in Knowledge-based Systems (IPMU) 2012 in Catania(Sicily), Italy, on July 11, 2012.

  • Foreword by the Editors

    It is without any kind of doubt that the work of Professor Lotfi A. Zadeh is of a greatrelevance in both the scientific and technological sides. His is a work that not onlymeant an important departure, but also a clear cut, from some old views on whichthinking and research were anchored. He also spread his work all around the worldthrough many lectures in many countries, and offered and continues to offer excitingnew views to open-eyed people wishing to do research without being blocked bysome old formal ways of looking at some theoretic or practical problems, impedingto pose them in a path allowing for its treatment.

    It could be said that Zadeh opened a new paradigm in, at least, Science and Tech-nology that was initially marked by the then surprising possibility of controllingphysical systems whose behavior is empirically described by a set of linguistic ruleswith imprecise terms, but not by an exact system of differential equations, when itexists, being usually computationally difficult to solve to obtain good enough valuesof its outputs. A new wave of researchers arose that, today, is followed by hundredsof researchers and engineers located in almost all parts of the world. Of this wavethose authors contributing to this book are but a sample.

    At the very beginning of the fuzzy adventure, just the presentation of the idea ofFuzziness not only provoked violent oppositions, as it is often the case for innova-tive ideas, but also triggered, and, in a sense forced, a rethinking of a few crucialand debated problems aroused at the beginning of last Century in the field of thefoundations of Mathematics and Logic. Also some papers tried to axiomatize thenotion of fuzzy set in order to take it as the starting point of a subsequent buildingof Mathematics. Besides remembering these first reactions to the then new emergingnotion, we can today certainly affirm that the notion of Fuzziness stands as one ofthe really new concepts that have recently enriched the world of Science in the samegood company of the ones of Computation, Information and Complexity, but also ofBohrs Complementarity. Science grows not only through technical and formal ad-vances on one side and useful applications on the other side, but also by introducingand assimilating new concepts in its corpus. These, in turn, produce new develop-ments and applications. Fuzziness has done all these things and will remain as oneof the few new concepts aroused in the XX Century.

    It is not usual that the founder of a new line of research can see in his life boththe theoretical growing of it, as well as the success of some technological applica-tions actually important from both the economical and the busin


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