The Fuzzy Systems Handbook: A Practitioner's Guide to Building, Using, and Maintaining Fuzzy Systems

672 Pages·1994·9.359 MB·English

by  Earl Cox

Compiling and Using the C++ Fuzzy
Modelling Code in The Fuzzy Systems Handbook
The C++ code included with The Fuzzy Systems Handbook comprises a
complete low-level fuzzy modeling environment. The functions are
designed for inclusion in a larger application framework and, by them-
selves, do not constitute an operational system. Examining the demon-
stration pricing model and inventory control demonstration programs,
included with the book, will show how this is done.
Please review the “READ.ME” file prior to using the software. It
provides important information, updates, and details regarding various
compilers.
If you discover problems in the actual operation of the code, please con-
tact me. My fax number is [phone]. My e-mail number is
[email protected].
Earl Cox
CEO
The Metus Systems Group
Icons and Topic Symbols
Throughout the handbook you will encounter a series of “sidebars” covering a wide
variety of special topics. Each topic is set off from the main text and is introduced by a
specific icon.
Code Discussion and Cross-reference. The diskette icon indicates that
this section deals with code models, programs, and software in general.
This icon usually means that a concept discussion is being tied back to the
actual supporting code in one or more of the libraries.
System Internals. The plumbing icon indicates that this section discusses
system internals. System interals refer to the data structures, control
blocks, interprogram linkages, process flow, and other details associated
with the way fuzzy modeling systems work.
Key Topics. A key icon indicates a detailed discussion on some important
aspect of the system. The nature of key topics covers a broad spectrum:
from hints and techniques that may not be obvious to detailed and off-line
explorations of concepts and philosophies.
System Construction. The hammer icon represents discussions centered
around the construction of models, applications, and high-level software
systems. This topic is not specifically concerned with function code or data
structures.
Practical Hints and Techiques. The wingnut (“nuts and bolts”) icon
indicates a discussion about the practical considerations of the current
topic. This includes programming techniques, system design consider-
ations, methodology approaches, etc.
Mathematical Topics. The ruler icon indicates a discussion of mathemati-
cal, logical, or algorithmic topics. This includes the underlying mathemat-
ics of fuzzy set theory, technical computer algorithms, topics in stability
and verification, as well as discussions of performance metrics. The icon is
only used for detailed discussed outside the main manual text.
Danger! Warning! The lightning bolt icon indicates a topic that could by
potentially dangerous to model intergrity, validation, or data. The danger
icon is also used to highlght harmful side effects that are not obvious. You should read
every danger topic carefully.
Reminders and Warnings. The reminder icon indicates a discussion of
important, but generally not obvious, points that the user must consider when
exploiting some portion of the fuzzy modeling technology.
The Fuzzy Systems Handbook by Earl Cox
Icons and Topic Symbols
Symbol Use
~ set NOT (also complement or inversion)
(cid:62) set AND (also intersection operator)
(cid:60) set OR (also union operator)
(cid:58) higher dimensional fuzzy space
[x,x,x] indicates a fuzzy membership value
(cid:101) member of a set (general membership)
poss(x) the possibility of event x
prob(x) the probability of event x
{x} crisp or Boolean membership function
• dyadic operator
(cid:106)(x) The expected value of a fuzzy region
(cid:109) fuzzy membership function
(cid:126) proportionality
(cid:109)[x] membership or truth function in fuzzy set
´ element from domain of fuzzy set
(cid:94) Cartesian product or space
˘ empty or null set
(cid:46) implication
(cid:96) logical AND
(cid:126) logical OR
(cid:111) summation
The Fuzzy Systems Handbook by Earl Cox
.
The
Fuzzy Systems
H a n d b o o k
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The
Fuzzy Systems
H a n d b o o k
A P r a c t i t i o n e r ’ s G u i d e t o B u i l d i n g ,
U s i n g , a n d M a i n t a i n i n g F u z z y S y s t e m s
E A R L C O X
Chappaqua, New York
AP PROFESSIONAL
BOSTON SAN DIEGO NEW YORK
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Contents iv
This book is printed on acid-free paper. ¥
Copyright ” 1994 by Academic Press, Inc.
All rights reserved.
No part of this publication may be reproduced or
transmitted in any form or by any means, electronic
or mechanical, including photocopy, recording, or
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permission in writing from the publisher.
All brand names and product names mentioned in
this book are trademarks or registered trademarks
of their respective companies.
BYTE Magazine quote on back cover taken from
“Put Fuzzy Logic to Work,” lon Udell,
BYTE Magazine, July 1994. (cid:211) McGraw-Hill, Inc.
AP PROFESSIONAL
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A Division of HARCOURT BRACE & COMPANY
United Kingdom Edition published by
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Library of Congress Cataloging-in-Publication Data
Cox, Earl.
The fuzzy systems handbook: a practitioner’s guide to building,
using, and maintaining fuzzy systems / Earl Cox.
p. cm.
Includes bibliographical references and index.
ISBN 0-12-194270-8
1. System design. 2. Adaptive control systems. 3. Fuzzy systems.
I. Title.
QA76.9.S88C72 1994
003'7--dc20 93-42608
CIP
Printed in the United States of America
94 65 96 97 IP 9 8 7 6 5 4 3 2
The Fuzzy Systems Handbook by Earl Cox