ADVANCES IN FUZZY SETS, POSSIBILITY THEORY, AND APPLICATIONS

Transcription

1 ADVANCES IN FUZZY SETS, POSSIBILITY THEORY, AND APPLICATIONS

2 ADVANCES IN FUZZY SETS, POSSIBILITY THEORY, AND APPLICATIONS Edited by Paul P. Wang Duke University Durham, North Carolina PLENUM PRESS NEW YORK AND LONDON

3 Main entry under title: Library of Congress Cataloging in Publication Data Advances in fuzzy sets, possibility theory, and applications. Includes bibliographical references and index. 1. Fuzzy sets-addresses, essays, lectures. I. Wang, Paul P. QA248.A '2 ISBN-13: e-isbn-13: DOl: / Plenum Press, New York A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

4 The Changes is a book From which one may not hold aloof. Its tao is forever changing Alteration, movement without rest, F10wing through the six empty places, Rising and sinking without fixed law, Firm and yielding transform each other. They cannot be confined within a rule, It is only change that is at work here. I Ching (Book of Changes)

5 PREFACE Since its inception by Professor Lotfi Zadeh about 18 years ago, the theory of fuzzy sets has evolved in many directions, and is finding applications in a wide variety of fields in which the phenomena under study are too complex or too ill-defined to be analyzed by conventional techniques. Thus, by providing a basis for a systematic approach to approximate reasoning and inexact inference, the theory of fuzzy sets may well have a substantial impact on scientific methodology in the years ahead, particularly in the realms of psychology, economics, engineering, law, medicine, decision-analysis, information retrieval, and artificial intelligence. This volume consists of 24 selected papers invited by the editor, Professor Paul P. Wang. These papers cover the theory and applications of fuzzy sets, almost equal in number. We are very fortunate to have Professor A. Kaufmann to contribute an overview paper of the advances in fuzzy sets. One special feature of this volume is the strong participation of Chinese researchers in this area. The fact is that Chinese mathematicians, scientists and engineers have made important contributions to the theory and applications of fuzzy sets through the past decade. However, not until the visit of Professor A. Kaufmann to China in 1974 and again in 1980, did the Western World become fully aware of the important work of Chinese researchers. Now, Professor Paul Wang has initiated the effort to document these important contributions in this volume and to expose them to the western researchers. A list of Chinese researchers in fuzzy set theory and applications is given in the appendix. The publication of this volume will certainly stimulate mutual exchanges of research ideas and results between Chinese and Western scientists and engineers working in the area of fuzzy sets and applications. K. S. Fu President, North American Fuzzy Information Processing Society Lafayette, Indiana December 1982 vii

6 ACKNOWLEDGEMENTS The recent opening of the People's Republic of China also opened for study the area of Chinese scientific advances. The researchers are grateful for this new opportunity resulting in a tremendous exchange of ideas which benefits both the Chinese and American people in addition to the universal world of science. This editor would like to acknowledge and to express his appreciation for the financial assistance he has received for international travel (summer 1981) from the Josiah Charles Trent Memorial Foundation, Inc. The funds for this grant were given to Dr. and Mrs. James Semans through a trust provided by Mrs. Sarah P. Duke. For a project of this nature, it was necessary to take a second trip to China (summer 1982) in order to fully understand the scope of the fuzzy set research activities there. It is important to realize that the support of academic leaders; such as Mr. Zhu Jiusi, President of Huazhong University of Science and Technology, and Mr. Wang Pin-Yang, Chief Engineer of the Electric Power Science Research Institute, is extremely crucial for Chinese research activities to flourish. The appreciation of the value of international communication of my late Dean of Engineering, Dr. Aleksandar Vesic should also be recognized. It is impossible to mention the names of all the researchers who have helped by offering suggestions about the content. Even more important, is their willingness in providing their best manuscripts to be included in this volume. However, I am profoundly grateful to Mr. Sam Earp of the E. E. Department at Duke University for many stimulating discussions in the course of putting these papers together. Dr. Enrigue H. Ruspini's assistance in preparing Chapter I which improves the overall presentation is also gratefully acknowledged. I also owe thanks to Mr. Wang Ju of U.C.L.A. and Academia Sinica for a portion of indexing work, and to Mr. Zhang Jinwen of Academia Sinica for providing much of the necessary information for the Appendix. I also want to thank Jane S. Culver for typing the manuscripts. ix

7 x ACKNOWLEDGMENTS Finally, I am indebted to my chairman Dr. H. Craig Casey, Jr. for his support. Paul P. Wang April 1983 in Durham, N.C.

8 CONTENTS Fuzzy Set Theory: Past, Present and Future Paul P. Wang, Sam Earp, and Enrigue H. Ruspini Advances in Fuzzy Sets - An Overview. Arnold Kaufmann A Survey of Some Aspects on the Research Work of Fuzzy Topology in China Pu Bao-ming and Liu Ying-ming Some Properties of Fuzzy Convex Sets Liu Ying-ming "Non-standard" Concepts in Fuzzy Topology Umberto Cerruti The Spaces of Fuzzy Probability and Possibility Zhende Huang and Tong Zhengxian An Algebraic System Generalizing the Fuzzy Subsets of a Set Cao Zhi-qiang From the Fuzzy Statistics to the Falling Random Subsets Wang Pei-zhuang On Fuzzy Relations and Partitions B. Bouchon and G. Cohen Fuzzy Set Structure with Strong Implication Zhang Jinwen Inference Regions for Fuzzy Propositions I.B. Tiirksen Fuzzy Tree Grammar and Fuzzy Forest Grammar Chu Shang-yong xi

9 xii CONTENTS Fuzzy Production Rules: A Learning Methodology L. Lesmo, L. Saitta, and P. Torasso Decision Support with Fuzzy Production Systems Thomas Whalen and Brian Schott Imprecision in Computer Vision Ramesh Jain and Susan Haynes Fuzzy Programming: Why and How? - Some Hints and Examples Henri Prade A Fuzzy, Heuristic, Interactive Approach to the Optimal Network Problem.... Didier Dubois Application of Fuzzy Set Theory to Economics Guo Quan Chen, Samuel C. Lee, and Eden S. H. Yu Use of Fuzzy Logic for Implementing Rule-Based Control of Industrial Processes E. H. Mamdani, J. J. stergaad, and E. Lembessis A New Approach to Design of Fuzzy Controller M. Sugeno and T. Takagi Advanced Results on Applications of Fuzzy Switching Functions to Hazard Detection.... Masao Mukaidono The Application of Fuzzy Set Theory to a Risk Analysis Model of Computer Security Wilker Shane Bruce and Abraham Kandel Fuzzy Models of Human Problem Solving. 377 William B. Rouse A Concept of A Fuzzy Ideal for Multicriteria Conflict Resolution Yee Leung Appendix I: Fuzzy Set Research in People's Republic of China Author Index 413 Subject Index 415