586 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
THE COMPARATIVE STUDY ON SYSTEM DYNAMICS
AND GREY SYSTEM THEORY
Qifar Wang Waizhou Huang
System Dynamics Group
Shanghai Institute of Mechanical Engineering
Shanghai, China
ABSTRACT
System dynamics created by professor Jay W. Forrester at MIT, is
a field which bases on system theory, absorbs the quintessence of
control theory, and draws support from computer simulation
technique. Established by professor Deng Julong at Central China
Institute of Science and Technology in 1982, grey system theory
derives its idea and methodology mainly from control theory and
operations research. Although system dynamics and grey system
theory both have their own features in methodology and processing
technique, there are still a lot of common points between them.
From the comparative study on these two fields, the paper arrives
at that it is not only necessary but also possible to infiltrate
and draw on the experiences of each other to develop themselves.
The new system analysis, modeling and decision-making approaches
have being developed with the development of science and
technology. System dynamics and grey system theory are two of
such new fields,
1, THE GENERAL DESCRIBTION OF SYSTEM DYNAMICS AND GREY SYSTEM
THEORY
System dynamics is a new field built by professor Jay W.
Forrester at MIT. Based on the deep study on economy and.
industrial organizations ( the system including people, finance
and technology), Forrester pointed out a lot of points of view
about the information feedback system and the basic system
components. The new cross field was founded based on system
theory, absorbed the quintessence of control theory and
information theory, and got help from computer simulation.
Grey system theory is the new theory founded by professor Deng
Julong at the Central China Institute of Science and Technology
in 1982. Professor Deng pointed out and developed the new
concepts of grey system based on the deep inspection of the
special system problems in which the known and unknown
information are both contained in the system, and created the new
theory which extends to the social economic system and combines
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automatic control science and the mathematics methods of
operations research.
System dynamics has developed its own theoretic system after 30
years development. Grey system theory is also formed the
theoretic system with its own characteristics although it is only
several year history. It can be seen that there are many aspects
in thinking methods and processing ways where one theory is
similar to, complement of and draws on the experiences on the
other after the comparative study on the theoretic system of
system dynamics and grey system theory, It is hopeful that such
comparative study can push them to develop further.
2. THE ANALYSIS METHOD COMPARISON BETWEEN SYSTEM DYNAMICS AND
GREY SYSTEM THEORY
1) The concept of system
System dynamics and grey system theory define that a system is
the sum of its parts that operate together for a common purpose.
Based on the definition above, " grey system " means the system
in which both known and unknown information are contained. It
should be pointed out that the human actions can be composed of
in the systems of interest.
2) The idea of system analysis
System analysis is the most important tool to make the system
structure be clear and to give the possibility for the system
simulation and computer modeling.
There is a lot of unknown information in the real world. The idea
of analysis is to get the unknown information as more as
possible, and to. make the unknown system be clear. The “ black
box ", " grey box " methods and grey system theory are all system
analysis methods developed when analyzing system. " Black box "
method means that system analysis is made by the way that from
the outside of the system, from the direct causal relationship,
and from the input-output relationship when the inner structure,
characteristics, and parameters of the system are all unknown and
impossible to analyze.the inner strueture.
It is true that there are some systems in the real world such as
the brain system of human being which are difficult to be
analyzed from the inner structure currently. "Black box" method
is a possible way to study them. But for social economic and
engineering systems, it is possible to analyses inner structure
directly. There are many advantages to analyze the system from
the inner structure, because the behavior of the system can be
easily grasped at higher degree of confidence by the way. From
the inner structure to analyze the system is the method which is
applied by system dynamics, From the micro-structure of system,
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system dynamics analyzes and grasps the characteristics and the
behavior of system based on the inner sructure, parameters, and
the general function of system.
"Grey box " means some of structures, parameters, and
characteristics of a system are known and the other unknown.
Professor Deng Jiulong supposes the box has the special meaning
of decoupling the inside from whe outside, but for the " grey box
“the known parts in it shoul¢e be used effectively, therefore he
created the new concept of grey system. It is not only to study
the causal and input-output relation of the system from the
outside behaviors, but also to study the inner structure,
parameters, and behaviors of system from the inside by grey
system theory. The later is more concerned for playing the role
of " white information “ as best as possible.
From the comparative study on the ideas of system analysis of
these two fields, it can be obviously found that system dynamics
and grey system theory both pay attention to studying the ianer
structure of system and to using the "white information " from
the inside of systew effectively. From the recognition process,
the system dynamics and grey system theory have the same process
gradually from unknown to a little bit understanding, then to
more understanding.
From the comparative study on the modeling of these two fields,
it can be found from the appearance of model that the model based
on grey system theory contains grey parameters, but the model
based on system dynamics does not. We should consider the later
model as the result of whiting system. To white the system is
realized by the continuously researching on the boundary
structure, and parameters of systems and applying some other ways
( including the experiences and judgements of human being ) to
estimate the parameters of system, The precision of whiting
process is not so perfect, because on one hand there is different
prejudice of human being in the whiting process, on the other
hand it is impossible to understand the inner structure and
parameters of system precisely even there is no any prejudice of
human being according to Heisenberg's principles of inprecise
measurement and Gédel's theorem of unperfect ability.
3) The method of system analysis
Grey system theory is the product of lengthening the points of
view and methods of control thecry to social economic system, so
the methods of system analysis of grey system theory continue to
use a series of analysis method of control theory. Such methods
include controllability, observability, stability analysis and
dynamic characteristic analysis of system.
The controllability of system mainly concerns the changable
property of the input to the state of system. It is meaningful to
the social economic system. Since the input of social economic
system include some policies. It is the worst if the input policy
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can not control the social economic system. Based on the method
of control theory, grey system theory studies the controllability
of grey system and gets some meaningful conclusion. System
dynamics also studies the controllability if necessary, and has
got success in some cases.
The observability of system mainly concerns the observable
property of system state directly from the system output. For
general systems, it is not easy to measure the system state
directly, it can only be measured from the output of system, so
it is significant to study the observability of system. For the
system of system dynamics involved, the study of observability of
system is not so important as grey system theory. The level
variables in system dynamics models stand for the system state
and have real meaning. Some system states are measurable, some
are not, the observation of system states cap be realized by
printing ali level variables in system dynamics modeis when
simulation, When some system state variables are unmeasurable, it
is necessary to study the observability when system states should
be measured and the observation of system states can be realized
by Kalman filtering and other methods, The study of observability
for grey system is significant. Because it can answer whether the
system state can be observed from the output when there are some
grey elements in the structure. If the grey system is observable,
it means the observability of system state does not change with
the change of grey elements.
The stability of system is one of the most important properties.
The higher stability, the higher ability of disturbance
resistance and vice versa, The problems grey system involved are
mostly linear problems. The scale of the problems are not very
large. The analysis methods are mainly time domain analysis. The
stability of grey system can be researched from the eigenvalue
analysis. The problems system dynamics involved are generally
large scale, nonlinear, so the concept of stability analysis is
more complex than that of grey system theory. System dynamics
applies time domain and frequency domain (the combinative study
on the properties of amplifier-frequence and period-frequence)
methods to analyze the stability of the linar system and the
system which can be linearized. System dynamics also apply the
frequency domain method to analyses the stability for the system
which can not be linearized or the stability can not be judged
after the linearization. Lyapunov first method is often applied
in system dynamics. Lyapunov second method can be also applied in
system dynamics for the problems of Lyapunov function which can
be searched by Krasovskii method.
The dynamic characteristic analysis concerns the sensitivety of
the change of inner structure to the change of system behavior.
Grey system theory applies.some methods derived from linear
control theory such as eigenvalue analysis to linear problems.
But eigenvalue analysis method is not the only one method in
system dynamics since the problems system dynamics handled are
large scale and nonlinear. Therefore the new methods with system
590 THE 1987 INTERNATIONAL CONFERENCE OF. THE SYSTEM DYNAMICS SOCITY. CHINA
dynamics character have developed--the dominant loop analysis and
sensitive parameters analysis. System dynamics considers that the
basic unit of system structure is feedback loop, and the behavior
of system is determined by the structure. Furthermore there are
some dominant loops in the structure which almost determine the
behavior of system, The dynamic behavior can be discoverd by the
way ‘of searching and analyzing the dominant loops. The special
software DYNASTAT has been developed to analyze the. dominant
loops in system dynamics. DYNASTAT can be conveniently applied to
search the dominant loops in nonlinear and large scale systems to
research the dynamic property of system, The dominant loop
analysis method in system dynamics is contributed to large scale
system theory. The idea of dominant loop analysis has general
meaning to large scale system.
After comparison of system analysis methods of the two fields, it
is obvious that based on nonlinear large scale system system
dynamics enlarges a series of analysis methods which originated
from modern control theory and creats some new methods with its
own feature, But grey system theory continues to use the analysis
method of modern control theory.
3. THE MODELING METHOD OF SYSTEM DYNAMICS AND GREY SYSTEM THEORY
System modeling is the preparatory step of decision-making. A
model which describes the basic structure of system provided the
fundamental for system simulation and decision-making.
The following points can be seen after the comparison of the two
fields.
1) The models of system dynamics and grey system theory are both
differential equations. The process of modeling in system
dynamics and grey system theory are similar to. The sequence of
the process is a) mental model, b) network model, c) quantitative
model, d) dynamic model, e) optimal model.
2) System dynamics considers nonlinear and large scale property.
So the system dynamics model can reflect nonlinear and large
scale property of system. Grey system theory is not so.strong in
dealing with nonlinear problems (at least currently). As there is
distance between linear large scale system theory and practical
application, grey system theory can only solve middle or small
scale systems successfully now. With the development of grey
system theory and large scale system theory, it may be used to
solve large scale problems in the near future.
3) Based on the overall analysis of system, system dynamics pays
attention to the fundamental components of system--information
feedback loop structure. System dynamics model is not only a
function simulation but also a structure simulation because
system dynamics pays attention to the function and structure of
systems simultaneously when modeling. System dynamics model is
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the structure--function model. System modeling way--from micro
structure to build fundamental structure and furthermore to
simulate and analyze the property, is different from the common
modeling way (black box method) and suitable to understand the
complex system problem. Although grey system theory overcome the
limitation of " grey box " and pays attention to the information
usage from the inner structure of system, it does not overcome
the limitation of function simulation way (black box). Grey
system theory models only reflect the function of system, it does
not consider the structure of system,
4) System dynamics pays attention to the judgement of human being
in modeling. Some of the parameters in model are estimated by the
experience of human being. System dynamics assumes that the
system behavior is mainly determined by inner structure and
parameter, and the structure is the most important factor to
determine the system behavior. System dynamics does not pay the
same attention to the estimation of all parameters. Some key
parameters (sensitive parameters) should be searched before
estimation of all parameters and should be estimated accurately,
The other parameters (nonsensitive parameters) can be estimated
roughly. System dynamics not only applies some common parameter
estimation methods such as Least Squares method, but also
develops some special parameter estimation methods such as Full
Information Maximum Likelihood Estimation .
Grey system theory pays more attention to accuracy data process
technique to determine the parameter of system. But it seems that
grey system theory does not pay enough attention to the
experience and judgement of human being. System dynamics and grey
system theory can draw on the experience of each other on the two
points above.
4, THE SIMULATION AND FORECAST IN SYSTEM DYNAMICS AND GREY SYSTEM
THEORY
System simulation can give different solution in different
conditions (system parameter, environment change and input
change). The decision maker can select the optimal or
quasi~optimal solution among them.
In fact, system solution can be found by the analytic method
without simulation for simple linear systems. The optimal
solution can be convinently found by such method. The special
software should be developed to deal with the complex computing
problems to reduce labor tension. This is the idea of grey system
theory. %
It is very difficult and even impossible to find analytic
solution for nonlinear or complex linear problems by analytic
method directly. As there are some difficult in computation, the
special software is not easy to develop.
592 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
It is grateful that grey system theory developed and applied the
effective data process technique in forecast. Some satisfied
results have been reached in use of residual information and the
higher accurat results in the short term forecast have also been
reached in use of residual identification information.
Compared with grey system theory, system dynamics pays much more
attention to simulation technique. The special simulation
language DYNAMO has been developed and ail nonlinear system
problems can be solved by it. As high speed computation of
computer and the DYNAMO ability of dealing with nonlinearity and
time delay, it is convenient and fast to apply DYNAMO to simulate
the different results of nonlinear, time delay, and large scale
problems in different conditions (structure parameter,
environment and input-output change). Another advantage DYNAMO
has is that the model built by DYNAMO corresponds, to the
structure of problems (variable, structure corresponding). The
simulation solution of system dynamics may be data output or
curve output. Based on DYNAMO, the imagination of decision maker
and system parameter change, environment change can be easily and
fast simulated on computer. So decision can be easily made after
the comparison of the output.
It is very difficult and even impossible to find the optimal
solution to nonlinear large scale syetem (especially to social
economic system). But as DYNAMO has the convenient and fast
simulation ability, it is possible to simulate some different
typical conditions. So some quasi-optimal solutions can be. found
among the simulation results corresponding to a series of
different policies, environment and condition change if such
changes and policies’ can be considered carefully by policy
designer, Such solutions are not optimal, but many conditions
including system environment and other changes have been
considered when. simulation, so they are the " optimal solution
we can find currently. Therefore we can consider system dynamics
as a powerful tool that can be used in laboratory to design and
analyze policy by decision maker, To some extent system dynamics
has promoted a revolution in research methods of social science.
"
The meaning of forecast in system dynamics is discussed under
given conditions, System dynamics pays. attention to the structure
research and builds model from the micro structure. Compared with
grey system theory, system dynamics has the function of long term
forecast. System dynamics and grey system theory have the similar
accuracy in short term forecast. In fact, it is not consistent
between the experience and judgement of human being and usage of
residual information, the long term forecast with lower accuracy
corressponding to short term forecast with higher accuracy. It
seems impossible to solve the contradiction above in methodology.
5. DECISION-MAKING IN SYSTEM DYNAMICS AND GREY SYSTEM THEORY
H. A. Simon considers that the decision-making of human being is
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partly rational, scientific and logic. That'’means decision maker
can only make decision based on the limited information souce
through the process of science and logics. Decision-making in
system dynamics and grey system theory can only be partly
rational, scientic and logic.
Except few simple systems, system dynamics considers that the
most decision-making process have been involved by human being.
As the careers and prejudice are different for different people,
it seems impossible to make optimal decision by decision maker.
System dynamics pays attention to the effect of human being when
decision-making and does not seek the optimal solution without
the effect of human being. The experiences and judgements of
decision makers have been used to conceptuate and analyze the
possible conditions in system dynamics, then the different
policies can be studied. In such a way, some selectable decisions
can be given to actural decision maker to make the last decision
based on their own experiences and judgements.
The decision theory of grey. system theory is mainly come from
operations research. The view of point of optimization has been
stressed in grey system theory. Grey system theory developed. the
linear program and nonlinear program in operation research to
grey linear program and grey nonlinear program, developed
regional planning theory to grey regional planning, and developed
game theory to grey situation decision-making.
It is expectful that a new effective theory and method which
based on system dynamics absorb advantages from other system
fields to form system thinking, simulation and search for optimal
in dealing with nonlinear. and complex system problems will be
developed in the near future.
From the preliminary comparative study between system dynamics
and grey system theory in the paper, it can be found that there
are many similar aspects in methodology and process techniques
between system dynamics and grey gystem theory. Some of them are
exact same, some of them are not, and some of them have large
difference. The tendency of infiltration and cross in the
development process of science and technology has been becoming
stronger and stronger. It is hopeful that the probability of
drawing on experience from all fields for each one will be
greater and greater with time.
REFERENCES
Forrester, Jay W., 1968. Principles of Systems. Mass.: The MIT
Press
Wang, Qifan., 1984, System Dynamics. Printed at Shanghai
Institute of Mechanical Engineering
594 THE 1987 INTERNATIONAL CONFERENCE OF THE SYSTEM DYNAMICS SOCITY. CHINA
Forrester, Jay W., 1980. Industrial Dynamics. Mass.: The MIT
Press
Deng, Julong., 1985. Grey System: In Society and Economy. The
National Defence Industry Press
Deng, Julong., 1985, Grey Contral System, The Central China
University of Science and Technology Press
Simon, H. A., 1985. The New Science of Management Decision.
(Translated into Chinese) The Chinese Social Science Press
Wang, Qifan., Philosophical Views and Basic Theories. of System
Dynamics. Proceedings of the 1986 China National System Dynamics
Conference.
Wang, Qifan., On the Statistical and Estimative Problems of the
Parameters of System Dynamics Model. Proceedings of the 1986
China National System Dynamics Conference.
