Fuzzy Sets in Approximate Reasoning and Information Systems
Approximate reasoning is a key motivation in fuzzy sets and possibility theory. This volume provides a coherent view of this field, and its impact on database research and information retrieval. First, the semantic foundations of approximate reasoning are
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THE HANDBOOKS OF FUZZY SETS SERIES Series Editors Didier Dubois and Henri Prade IRIT, Universite Paul Sabatier, Toulouse, France
FUNDAMENTALS OF FUZZY SETS, edited by Didier Dubois and Henri Prade MATHEMATICS OF FUZZY SETS: Logic, Topology, and Measure Theory, edited by Ulrich Hohle and Stephen Ernest Rodabaugh FUZZY SETS IN APPROXIMATE REASONING AND INFORMATION SYSTEMS, edited by James C. Bezdek, Didier Dubois and Henri Prade FUZZY MODELS AND ALGORITHMS FOR PATTERN RECOGNITION AND IMAGE PROCESSING, by James C. Bezdek, James Keller, Raghu Krisnapuram and Nikhil R. Pal FUZZY SETS IN DECISION ANALYSIS, OPERATIONS RESEARCH AND STATISTICS, edited by Roman Slowinski FUZZY SYSTEMS: Modeling and Control, edited by Hung T. Nguyen and Michio Sugeno PRACTICAL APPLICATIONS OF FUZZY TECHNOLOGIES, edited by HansJUrgen Zimmermann
FUZZY SETS IN APPROXIMATE REASONING AND INFORMATION SYSTEMS edited by
James
c. Bezdek
University o/West Florida
Didier Dubois lRIT, CNRS & University o/Toulouse III and
Henri Prade IRIT, CNRS & University o/Toulouse III
.., ~
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
Fuzzy sets in approximate reasoning and information systems / edited by James C. Bezdek, Didier Dubois and Renri Prade. p. cm. -- (The Randbooks of fuzzy sets series ; FSRS 5) Includes bibliographical references. ISBN 978-1-4613-7390-2 ISBN 978-1-4615-5243-7 (eBook) DOI 10.1007/978-1-4615-5243-7
1. Expert systems (Computer science) 1. Bezdek, James C., 1939-. sets. III. Prade, Renri M. IV. Series. QA76.76.E95F8866 1999 006.3 3--dc21
2. Reasoning. 3. Fuzzy II. Dubois, Didier.
I
99-16664 CIP
Copyright © 1999 by Springer Science+Business Media New York Originally published by Kluwer Academic Publishers in 1999 Softcover reprint of the hardcover 1st edition 1999
AlI rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC
Printed an acid-free paper.
Contents
Series Foreword Contributing Authors
xi xiii
Introduction
Didier Dubois, Henri Prade, James Bezdek
PART I
REASONING
1 Fuzzy Sets and Possibility Theory in Approximate and Plausible 15 Reasoning Bernadette Bouchon-Meunier, Didier Dubois, L1uis Godo and Henri Prade
1.1
Introduction 15 1.1.1 The Emergence of Fuzzy Set-Based Approximate Reasoning 16 1.1.2 Organization of the Chapter 17
1.2
A Refresher on Possibility Theory ar:ld Fuzzy Connectives 18 1.2.1 A Short Course on Possibility Theory 18 1.2.2 Fuzzy Connectives: Negations, Conjunctions and Disjunctions 25 1.2.3 Fuzzy Implications 27
1.3
Representation of Fuzzy Statements 1.3.1 Linguistic Variables 1.3.2 Linguistic Modifiers 1.3.3 Modelling Elementary Fuzzy Statements 1.3.4 Compound Fuzzy Statements
1.4
43 Representation of Qualified and Quantified Fuzzy Statements 1.4.1 Fuzzy Truth-Values 43 1.4.2 Truth Qualified Statements 46 1.4.3 Gra
