Fuzzy Logic State of the Art

Fuzzy Logic: State of the Art covers a wide range of both theory and applications of fuzzy sets, ranging from mathematical basics, through artificial intelligence, computer management and systems science to engineering applications. Fuzzy Logic will be of

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THEORY AND DECISION LIBRARY

General Editors: W. Leinfellner (Vienna) and G. Eberlein (Munich) Series A: Philosophy and Methodology of the Social Sciences Series B: Mathematical and Statistical Methods Series C: Game Theory, Mathematical Programming and Operations Research Series D: System Theory, Knowledge Engiheering and Problem Solving

SERIES D: SYSTEM THEORY, KNOWLEDGE ENGINEERING AND PROBLEM SOLVING VOLUME 12

Editor: R. Lowen (Antwerp); Editorial Board: G. Feichtinger (Vienna), G. J. Klir (New York) O. Opitz (Augsburg), H. J. Skala (Paderborn), M. Sugeno (Yokohama), H. J. Zimmermann (Aachen). Scope: Design, study and development of structures, organizations and systems aimed at formal applications mainly in the social and human sciences but also relevant to the information sciences. Within these bounds three types of study are of particular interest. First, formal definition and development of fundamental theory and/or methodology, second, computational and/or algorithmic implementations and third, comprehensive empirical studies, observation or case studies. Although submissions of edited collections will appear occasionally, primarily monographs will be considered for publication in the series. To emphasize the changing nature of the fields of interest we refrain from giving a clear delineation and exhaustive list of topics. However, certainly included are: artificial intelligence (including machine learning, expert and knowledge based systems approaches), information systems (particularly decision support .systems), approximate reasoning (including fuzzy approaches and reasoning under uncertainty), knowledge acquisition and representation, modeling, diagnosis, and control.

The titles published in this series are listed at the end of this volume.

FUZZYLOGIC State ofthe Art edited by

R.LOWEN University ofAntwerp, Antwerp, Belgium

and

M. ROUBENS Universitlff de Liege, Liege, Belgium

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

Library of Congress Cataloging-in-Publication Data Fuzzy logie state of the art / edited by R. Lowen and M. Roubens. p. em. -- (Theory and deeision library, Series D, System theory, knowledge engineering, and problem solving ; v. 12) ISBN 978-94-010-4890-3 ISBN 978-94-011-2014-2 (eBook) DOI 10.1007/978-94-011-2014-2 1. Fuzzy sets--Congresses. 2. Fuzzy systems--Congresses. r. Lowen, R. (Robert) II. Roubens, Mare. III. Series. QA248.F856 1993 511.3--dc20 93-15889

ISBN 978-94-010-4890-3

Printed an acid-free paper

AH Rights Reserved © 1993 Springer Science+Business Media Dordrecht

Originally published by Kluwer Academic Publishers in 1993 Softcover reprint ofthe hardcover Ist edition 1993 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.

TABLE OF CONTENTS Preface

ix

I. MATHEMATICS Nonmonotonicity, Fuzziness, and Multi-Values P. Doherty and D. Drianko