Spatial Analysis and Planning Under Imprecision

382 Pages·1988·3.31 MB·English

by  Y. Leung and Ake E. Andersson (Auth.)

Studies in
Regional Science
and Urban Economics
Series Editors
ÄKEE.ANDERSSON
WALTER ISARD
PETER NIJKAMP
Volume 17
NORTH-HOLLAND -AMSTERDAM · NEW YORK · OXFORD »TOKYO
Spatial Analysis
and Planning
under Imprecision
YEE LEUNG
Department of Geography
The Chinese University of Hong Kong
Shatin, N.T.
Hong Kong
cm
1988
NORTH-HOLLAND -AMSTERDAM · NEW YORK · OXFORD «TOKYO
©ELSEVIER SCIENCE PUBLISHERS B.V., 1988
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or
transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,
without the prior permission of the copyright owner.
ISBN: 0 444 70390 x
Publisher:
ELSEVIER SCIENCE PUBLISHERS B.V.
P.O. Box 1991
1000 BZ Amsterdam
The Netherlands
Sole distributors for the U.S.A. and Canada:
ELSEVIER SCIENCE PUBLISHING COMPANY, INC.
52 Vanderbilt Avenue
New York, N.Y. 10017
U.S.A.
LIBRARY OF CONGRESS
Library of Congress Cataloging-1n-Publication Data
Leung, Yee.
Spatial analysis and planning under imprecision / Yee Leung.
p. cm. — (Studies in regional science and urban economics ;
v. 17)
Bibliography: p.
Includes index.
ISBN 0-444-70390-X (U.S.)
1. Spatial analysis (Statistics) 2. Fuzzy sets. I. Title.
II. Series.
QA278.2.L483 1988
519.5'36~dc19 87-36007
CIP
PRINTED IN THE NETHERLANDS
To My Family
Vll
PREFACE
A baffling issue in the analysis of human behavior in
space and time is the seemingly incompatible nature of
objectivity and subjectivity, precision and imprecision,
simplicity and complexity, certainty and uncertainty, as
well as abstraction and realism. The attempt to analyze the
intertwining of subjectivity, imprecision, complexity, and
uncertainty (within human systems in general and spatial
systems in particular) with objective, precise, simple, and
deterministic mathematical systems gives rise to a certain
sense of dissatisfaction.
Over the years, significant spatial theories and models
under certainty have been quite successfully advanced through
the use of classical mathematics. Probability and stochastic
processes have further extended our abilities in analyzing
spatial behavior under randomness. Though our achievements
have been gratifying in terms of formalism, we are still quite
remote from an adequate description in terms of realism.
In our quest for objectivity, simplicity, and precision,
we customarily fit spatial behavior to rigid mathematical
models which make no provision for systems complexity and the
imprecision in our cognition, perception, valuation, and
decisionmaking processes. Human subjectivity and imprecision
have conventionally been regarded as absurd in scientific
investigations. Being precise has been a virtue of science.
Valuation is almost a forbidden word in formal models. Our
unabating effort in achieving higher level of precision has
been the instrument of spectacular advancements in the
physical sciences.
Following the path of the physical sciences, social
scientists have come to believe that human systems are also
precise in nature and can be efficiently analyzed by classical
mathematics. To be precise, we have attempted to force
artificial precision on imprecise phenomena and processes, and
in so doing have lost the intrinsic imprecision in human
systems in search of precision as a goal. In addition, we have
failed to realize that our ability to be precise diminishes as
the system becomes more complex. In cases of extreme complexity
precision is usually an impossibility. Spatial models which
neglect these intrinsic characteristics tend to be over-
simplified, too mechanical, and too inflexible to give an
adequate description of the complex and elastic real world.
To have a closer approximation to and control of our
spatial systems, it is essential to restore human values and to
Vlll Preface
treat imprecision with rigor in theory and model constructions.
Appropriate operational models should be able to mimic human
behavior in space and time. The behavioral approach for example
is developed for the purpose of making formal models more
appropriate to the human condition. Most behavioral models,
however, appear to be either too loose or too superficial in
terms of formalism. The lack of a cohesive mathematical system
which enables formal analysis of imprecise spatial behavior is
perhaps a major obstacle for behavioral models to be regarded
as elegant formalizations of spatial systems with operational
values. It is therefore imperative to have a system which
renders mathematical representations of imprecise human
behavior.
Among existing methods fuzzy set theory appears to be a
mathematical system which is instrumental in constructing
formal models of imprecise spatial behavior. It allows us to
restate the importance of treating human subjectivity, albeit
imprecise, in model formulations. It can also provide a bridge
between verbal and formal models. Under fuzzy set theory,
the human system is a flexible system within which cognition,
perception, thought, reasoning, and behavior are a matter of
degree.
Since the inception of fuzzy set theory in 1965, its
applications in information science, computer science, control
engineering, management science, operations research, and
formal logic have been phenomenal. Similar developments never-
theless have not been taking place in social science in general
and spatial analysis and planning in particular, although human
behavior is the subject of analysis in these disciplines.
Fragmentary research and the relatively slow dissemination of
fuzzy set theory in these fields naturally lead to confusion,
ambivalence, and misunderstanding.
Though there are a few books on fuzzy set theory, they do
not address the issues of imprecision in spatial analysis and
planning. The undertaking of the present monograph was
triggered by my perception of such a void in our literature.
My purpose is to put the fuzzy set approach in perspective. It
involves the reexamination of conventional concepts and the
laying of a foundation for fuzzy set theoretic spatial analysis
and planning under imprecision.
This monograph is written for geographers, regional
scientists, spatial economists, urban and regional planners,
fuzzy set researchers, and other interested social scientists.
It is of course difficult to satisfy such a variety of readers.
I hope the monograph can serve as a stimulus for a more compre-
hensive effort in analyzing human behavior in space and time.
I would like to thank Dr. Walter Isard for his open-
mindedness and continual encouragement of this project. Dr.
Peter Nijkamp's comments and his enthusiasm in having the
monograph refereed for publication in the present series is
deeply appreciated. I am also grateful for Dr. Peizhuang
Wang's detailed analysis and Dr. Manfred Fischer's comments on
the earlier draft. To Dr. Claude Ponsard goes my deepest
appreciation for his in-depth comments and suggestions on the
early and final drafts. I remain of course responsible for all
errors and deficiencies.
Preface ix
My deepest gratitude goes to Mrs. Jane Wan for typing and
re-typing the entire monograph with patience and excellence,
and to Mr. See-lou Too for his professionally done illustra-
tions. I also thank Miss Ho-kwan Lo for her professional
indexing.
Y. Leung
1
CHAPTER 1
INTRODUCTION
1.1. ON SYSTEMS COMPLEXITY AND IMPRECISION
Human systems in general and spatial systems in particular
are complex systems with omnipresence of subjectivity, incom-
pleteness, and imprecision. No matter what we are studying, an
individual, a firm, a group, a city, a region, a nation, or the
whole world, encountering awesome complexities is ordinarily
the rule rather than the exception. In general, spatial systems
at the micro, meso, and macro scales are too complex and valua-
tive for precision to be effective and deterministic statements
to be realistic.
At the micro scale, we are usually concerned with
decisions of an individual. Job search, residential choice,
location and operation of a firm are typical examples. Taking
an individual's job search as an example, to be completely
certain, he needs to amass precise information on all aspects
s
of the job market in the context of space and time. Based on
the availabilities of jobs, differences in wages, job stabili-
ties, prospects, living standards, and the living environments,
he then decides on the one which somehow can optimize or
satisfy a set of criteria or a composite criterion which he set
for a desirable job.
With limited amount of time, financial resources, and
mental capacity, acquiring complete and precise information on
these aspects within a complicated job market is impossible.
Therefore, information is never complete and is generally
imprecise. The job-search process is often based on approxima-
ted data.
In choosing a job, the criteria are usually imprecise.
2 Introduction
Under the utility maximizing principle, for example, "utility"
is a term with imprecise denotation. Even if the concept makes
sense to the individual, it is extremely difficuilt for him to
fathom what "utility" precisely means to him. Thus, utility
maximization is actually a fuzzy criterion guiding the
decisionmaking process.
Instead of employing a composite criterion such as
utility, a job seeker may want to base his decision on how well
the job satisfies a set of criteria such as wage, location,
work hours, job security, and prospect. A valuative decision
rule such as "high wage, convenient location, relatively short
work hours, secure, and good prospect" might be formulated as a
standard to evaluate plausible jobs. Again, the rule is fuzzy
because high, convenient, relatively short, secure, and good
are imprecise subjective valuations. They, however, carry
significant meanings and play an important role in the
decisionmaking process.
To elaborate my argument, residential choice is another
common micro-scale spatial decision in which complexity, valua-
tion, and imprecision are rampant. The system is complex
because residential choice, similar to job search, is not inde-
pendent of other basic living preferences such as those on job,
education for children, life style, and amenities. Within the
system, they are highly interdependent. To be completely
certain about a decision, obtaining precise information on the
availabilities of housing units, differences of rents or sale
prices, housing qualities, public service provisions, ameni-
ties, and crime rates in all localities is necessary. With
time and money constraints, information gathered is again
imperfect. For example, an individual may only know the
approximate housing stock, approximate rents or sale prices in
the market, rough descriptions of public service provisions and
crime rates, and subjective valuations of housing qualities and
amenities.
In making a decision, a sought after house has to satisfy
a value-based standard such as "short distance from home, high
quality, moderate rent or sale price, good public services,
quiet and clean neighborhood with low crime rate". Instead of
On Systems Complexity and Imprecision 3
making a precise judgement of distance, quality, rent or
sale price, public services, amenities, and crime rate, we
conceptualize them by fuzzy categories such as short, high
f
moderate, good, quiet and clean, and low which human brains can
process effectively. Again, we can cope with these complexities
and imprecisions and are able to make a decision.
The behavior of an organization such as a firm, is again a
micro-scale behavior of high complexity. In the locational
analysis of a firm, for example, complexity is intertwined with
imprecision and subjectivity. To find a location which can
maximize its profit, a firm needs to obtain perfect information
on the locations and availabilities of resources, locations of
labors with respect to their costs, skills, and work morales,
locations of markets, consumer preferences, as well as trans-
port systems in terms of modes, routes, and costs. Our experi-
ences have shown that such a task is impossible. While complete
and precise information is beyond reach, incomplete and impre-
cise information is what a firm has to settle for.
If the objective is to maximize profit or minimize cost,
it is quite a clear-cut locational rule provided that unit pro-
fits or unit costs can be precisely determined. If a firm pre-
fers the satisfaction principle to the optimization principle,
a fuzzy goal such as "Total profit should be approximately 10
million dollars11, or "Total costs should be below 2 million
dollars as much as possible^ is specified. Apparently, subjec-
tivity and flexibility exist in human thought and locational
decisions are based on imprecise rules.
Expanding our spatial context to the behavior of an inter-
national trade firm, the decisionmaking environment is even
more complex. To be certain, a firm needs to have perfect
information on the national and international markets in terms
of productions, consumptions, price differentials, and means of
transportation. However, such a perfection seldom exists in
the real world. Partial and imprecise information is the
reality international trade firms have to accept. Their
decisionmaking process is embedded with imprecision and sub-
jectivity. It is again due to our ability to reckon, think,
reason, and communicate globally with imprecise information,