Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems

405 Pages·1980·9.872 MB·English

by  Professor Paul P. Wang, Professor S. K. Chang (auth.), Paul P. Wang, S. K. Chang (eds.)

FUZZY SETS
Theory and Applications to Policy
Analysis and Information Systems
FUZZY SETS
Theory and Applications to Policy
Analysis and Information Systems
Edited by
Paul P. Wans
Duke University
Durham, North Carolina
and
S. K. Chans
University of Illinois
Chicago, Illinois
Plenum Press· New York and London
Library of Congress Cataloging in Publication Data
Symposium on Policy Analysis and Information Systems, Duke University, 1980.
Fuzzy sets.
Includes index.
1. Fuzzy sets-Congresses. 2. Policy sciences-Congresses. 3. Social systems
Congresses. 4. System analysis-Congresses. I. Wang, Paul P. II. Chang, Shi Kuo,
1944- III. Title.
QA248.S971980 511.3'22 80-19934
ISBN-13: 978-1-4684-3850-5 e-ISBN-13: 978-1-4684-3848-2
DOl: 10.1007/978-1-4684-3848-2
Proceedings of the SYmposium on Policy Analysis and Information Systems, held at Duke
University, Durham, North Carolina, June 28-30, 1980.
© 1980 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1980
A Division of Plenum Publishing Corporation
227 West 17th Street, New York, N.Y. 10011
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
FOREWORD
As the systems which form the fabric of modern society become
more complex and more interdependent, the need for the understanding
of the behavior of such systems becomes increasingly more essential.
What are the causes and possible cures for the worldwide inflation
which is posing a serious threat to the economic stability and social
order of both developed and underdeveloped countries? What are the
trade-offs between the urgent need for additional sources of energy
and the risks posed by the proliferation of nuclear reactors? How
can one devise mass transportation systems which are fast, comforta
ble, convenient, and yet not prohibitively expensive? These issues
are but some of the more visible problems posed by what might be
called the crisis of undercoordination--a crisis rooted in the widen
ing gap between the degree of interdependence in the systems of modern
society and the degree of coordination which libertarian societies are
willing to tolerate. The disquieting implication of this crisis is
that to achieve stability through coordination may necessitate the
imposition of pervasive controls which may be hard to accept by
societies steeped in the democratic tradition.
Viewed in this perspective, the need for developing a better
understanding of the behavior of large-scale societal systems presents
a problem of much more than purely academic importance. During the
past two decades (and especially since the advent of large-scale com
puters which can solve hundreds and even thousands of nonlinear dif
ference equations at low cost and with high reliability) considerable
progress in our ability to model the behavior of large-scale systems
has been achieved. However, a problem which is of central importance
to the analysis of large-scale systems, and which has not been solved
satisfactorily by conventional probability-based techniques, is that
of characterizing the behavior of systems in which the sources of
uncertainty and imprecision are, for the most part, non-statistical
in nature. It may well be the case that almost all societal systems
fall into this category.
The theory of fuzzy sets, which in one way or another relates to
all of the papers in the present volume, may be regarded as a body of
concepts and techniques for dealing with the imprecision and uncer
tainties which are associated with classes in which the transition
from membership to nonmembership is gradual rather than abrupt.
v
FOREWORD
Such classes play an essential role in human cognition, and it is for
this reason that the theory of fuzzy sets--as well as the theory of
possibility which is based on it--have a high degree of relevance to
policy analysis and information systems. In the case of such systems,
cognition, reasoning and communication form the cornerstones of their
foundation.
In application to policy analysis and information systems, it is
important to recognize that probability-based methods, on the one
hand, and fuzzy-set-theoretic (and especially possibility-based
methods) on the other, are complementary rather than competitive.
Thus, in most cases it is not correct to assert that a classical
probability-based technique is superior to a method provided by fuzzy
set theory, or vice-versa, since the domains of applicability of the
two theories are disjoint rather than coextensive. What is true, how
ever, is that in dealing with issues relating to policy analysis and
information systems, one frequently encounters a mixture of probabi
listic and possibilistic phenomena which call for a combination of
probability-based and possibility-based methods for their analysis.
Thus, in the years ahead, we are likely to witness a coalescence of
probabilistic and possibilistic techniques into a broader theory which
will be applicable to the entire spectrum of types of uncertainties
and imprecision. Such a theory would be particularly useful in pro
blems involving forecasting, analysis of evidence and decision-making
under uncertainty.
The papers presented in this volume address a broad variety of
problems arising in the analysis of systems in which the fuzziness of
goals, constraints and interrelations plays an important role. The
editors of this volume, Professors Paul Wang and S. K. Chang, have
done an excellent job of organizing the volume and they, together
with the authors, deserve a note of thanks from all of us for making
an important contribution to the advancement of the theory of fuzzy
sets and its application.
Professor Lofti A. Zadeh
Department of Electrical Engineering
and Computer Science
University of California
Berkeley, California 94720
CONTENTS
INTRODUCTION
Fuzzy Sets: Theory and Application to Policy
Analysis and Information Systems •.•.••.••.•.•• 3
P. P. Wang andS. K. Chang
SECTION I: THEORY
Minkowski Functionals of L-Fuzzy Sets ••.•.•••..••.•••..• 13
U. Hoble
Characterization of Fuzzy Measures by
Classical Measures •••.•.•.•••..•••••..••.•.••• 25
E. P. Klement
Necessary and Sufficient Conditions for the
Values of a Function of Fuzzy
Variables to Lie in a Specified
Subinterval of [0,1] ••••.•••.••.•••.•••••.•.•• 35
L. L. Scott
Fuzzy Logic and Non-Distributive Truth Valuations •..•.•. 49
D. McGoveran
New Results about Properties and Semantics of
Fuzzy Set-Theoretic Operators ••••••..•...•••.. 59
D. Dubois and H. Prade
On Potential Tautoligies in k-Valued Calculi
and Their Assessment by Means of
Normal Forms .....••.....•....•....•.•..•...... 77
V. Pinkava
Developments in the Wake of the
Theory of Possibility 87
E. Hisdal
vii
viii CONTENTS
Fuzzy Dynamical Systems and the Nature
of Their Solutions •••.••••••••.•••••••••••••• 93
A. Kandel
Abstract of Notes on Logics of Vagueness
and Some Applications ••.••••••.••••••••.••••• 123
D. H. Sanford
SECTION II: APPLICATIONS
Fuzzyism and Real World Problems 129
R. Jain
Fuzzy Statistics and Policy Analysis •••.•••••.•••..•••• 133
A. Kandel
An Outline of Fuzzy or Possibilistic Models
for Queuing Systems •••••••••••..•••••••.••••• 147
H. Prade
~I.
Operations Research with Fuzzy Data ••••.••••••••••••••• 155
H. M. Prade
Satisfaction and Fuzzy Decision Functions ••.••..••••••• 171
R. Yager
Experiments on Character Recognition Using
Fuzzy Filters .••..•.••.••..•.••.•••.•..•••••• 195
P. P. Wang and C. Y. Wang
A Self-Adaptive Fuzzy Recognition System for
Speech Sounds •••••••••••••••.••••••••..•••••• 223
S. K. Pal and D. D. Majumder
Sampling and Interpretation of Atmospheric Science
Experimental Data ••••••.••.•••.••..••...•.••. 231
R. W. Gunderson and J. D. Watson
Process Control Using Fuzzy Logic ..•.•.•••••••.•••••••• 249
D. H. Mamdani and B. S. Sembi
Fuz,zy Sets and Possibility Theory in Reliability
Studies of Man-Machine Systems ••••••..•••••.• 267
B. B. Chaudhuri and D. D. Majumder
Fuzzy Cost/Benefit Analysis ••.••••.••.•..••••.•••••••.• 275
L. A. Neitzel and L. J. Hoffman
CONTENTS ix
A Fuzzy Analysis of Consensus in Small Groups 291
B. Spillman, R. Spillman, and J. Bezdek
On Modeling Interpersonal Communications ••...•.•.•••.•. 309
R. Yager
Application of Fuzzy Decision-Making Models
for Determining Optimal Policies in
in "Stable" Integrated Regional
Developmen t ••...••.••.••.•.•..•..•••.•••...•• 321
J. Kacprzyk and A. Straszak
A Fuzzy Set Procedure for Project Selection
with Hierarchical Objectives ..••...•.•....... 329
Y. Leung
Relational Products as a Tool for Analysis
and Synthesis of the Behavior of
Complex Natural and Artificial
Systems ••••.••..••.••.•......•••.•••....•.•.. 341
W. Bandler and L. J. Kohout
Concept Structure and its Distortion in
the Communication and Formation
Process of Morality Concept ..••....••.•.•...• 369
M. Oda, T. Shimomura, and B. F. Womack
Fuzzy Concepts in the Analysis of Public Health Risks .. 391
T. B. Feagans and W. F. Biller
INDEX .....•.......•......................•..•.•........ 405
INTRODUCTION
FUZZY SETS: THEORY OF APPLICATIONS TO POLICY ANALYSIS AND
INFORMATION SYSTEMS
Professor Paul P. Wangl and Professor S. K. Chang2
Department of Electrical Engineeringl
School of Engineering
Duke University
Durham, NC 27706
2
Knowledge Systems Laboratory
Department of Information Engineering
University of Illinois at Chicago Circle
Chicago, IL 60680
INTRODUCTION
In this volume, we present a spectrum of original research works
ranging from the very basic properties and characteristics of fuzzy
sets to specific areas of applications in the fields of policy an
alysis and information systems. The first part, theory, presents
some fine added contributions toward a deeper basic understanding
of fuzzy set theory and serves to enrich set theory in the direc
tion of maturity and completeness of its theoretical development.
The Minkowski functional or gauge of an ordinary set plays an
important part in several areas of mathematics. In the first paper,
Hohle introduces the concept of Minkowski functionals to the case of
L-fuzzy sets. The contribution of Hohle represents a fine addition
to our fundamental understanding of L-fuzzy sets. His work can be
summarized in the form of a theorem stating that there exists a bi
jection from the set of all absolutely convex, closed, L-fuzzy 0-
neighborhoods onto the set of all fuzzy continous L-probalistic
semi-norms. The introduction of Minkowski functionals of L-fuzzy
sets provides an important theoretical prerequisite for the appli
cation of fuzzy set theory to optimization techniques for practical
usage.
3