Fuzzy Relation Equations and Their Applications to Knowledge Engineering
It took many decades for Peirce's coneept of a relation to find its way into the microelectronic innards of control systems of eement kilns, subway trains, and tunnel-digging machinery. But what is amazing is that the more we leam about the basically simp
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THEORY AND DECISION LIBRARY General Editors: W. Leinfellner and G. Ebedein Series A: Philosophy and Methodology of the Social Sciences Editors: W. Leinfellner (Technical Universtiy of Vienna) G. Eherlein (Technical University of Munich) Series B: Mathematical and Statistical Methods Editor: H. Skala (University of Paderborn) Series C: Game Theory, Mathematical Programming and Operations Research Editor: S. H. Tijs (University ofNijmegen) Series D: System Theory, Knowledge Engineering and Problem Solving Editor: W. Janko (University of Economics, Vienna)
SERIES D: SYSTEM THEORY, KNOWLEDGE ENGINEERING AND PROBLEM SOLVING Volume 3
Editor: W. Janko (Vienna) Editorial Board G. Feichtinger (Vienna), H. T. Nguyen (Las Cruces), N. B. Nicolau (Palma de Mallorca), O. Opitz (Augsburg), H. J. Skala (Paderborn), M. Sugeno (Yokohama). Scope This series focuses on the design and description of organisations and systems with application to the social sciences. Formal treatment of the subjects is encouraged. Systems theory, information systems, system analysis, interrelated structures, program systems and expert systems are considered to be a theme within the series. The fundamental basics of such concepts inc1uding computational and algorithmic aspects and the investigation of the empirical behaviour of systems and organisations will be an essential part of thls library. The study of problems related to the interface of systems and organisations to their environment is supported. Interdisciplinary considerations are welcome. The publication of recent and original results will be favoured.
For a list of titles published in this series, see final page.
FUZZY RELATION EQUATIONS AND THEIR APPLICATIONS TO KNOWLEDGE ENGINEERING by
ANTONIO DI NOLA and SALVATORE SESSA Universita di Napoli, Facolta di Architettura, Napoli, 1taly
WITOLD PEDRYCZ University 01 Manitoba, Department 01 Electrical Engineering, Winnipeg,
Canada
and
ELlE SANCHEZ Universite Aix-Marseille 11, Faculte de Medecine, Marseille, France
Forewordby
LOTFI A. ZADEH
University 01 California, Berkeley, U.S.A.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging in Publication Data Fuzzy relation equations and their appl ications to knowledge engineering ; Antonio DI Nola ... let al.]. p. cm. -- (Theory and decision library. Serles D. System theory, knowledge engineering, and problem solvlng) Inc 1udes b i b 1 i ograph 1 es and i ndexes. ISBN 978-90-481-4050-3 ISBN 978-94-017-1650-5 (eBook) DOI 10.1007/978-94-017-1650-5
1. Expert systems (Computer sclence) Nola, Antonlo. II. Serles.
2. Fuzzy systems.
QA76.76.E95F886 1989 006.3'3'01511322--dc20
1. DI
89-34246
ISBN 978-90-481-4050-3
printed on acid free paper
AII Rights Reserved © 1989 Springer Science+Business Media Dordrecht Originally pub1ished by Kluwer Academic Publishers in 1989 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 a
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