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i
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Integration of System Dynamics and Rule Based
Reasoning Mechanism
Yi-Ming Tu
Naeyi Shiao
Institute of Information Management
National Sun Yat-Sen University
Taiwan, R.O.C.
Abstract
After providing a framework for integration of System Dynamics and Expert Systems, this paper builds
theoretical bases to integrate three main features of rule based reasoning mechanism into conventional
System Dynamics models. Then we start to modify the System Dynamics modeling tools to adopt the
integrated features. To illustrate, we demonstrate a prototype for integrated theories above.
Introduction
System Dynamics (SD) has been successfully applied to solve many problems for years. However, the
methodology itself seems to have less progress than its applications. This paper tries to broaden the
modeling capability of SD through rule based reasoning mechanism in Expert Systems (ES).
First, we depict the framework of ES aid to SD ; then integrate rule based reasoning mechanism into the
SD model, modify SD modeling process. To illustrate, we provide a prototype demonstrated for integrated
features,
Expert Systems Aid to System Dynamics
In SD modeling process, we usually follow the four steps below:
1. Conceptualization : focusing on impotrtant elements of the real world problems, utilizing causal diagram
to describe the causal feedback relationship among elements.
2. Formulation : partitioning causal diagram, determining levels, rates, auxiliary variables, and parameters
by SD diagram, then preparing to compile and execute the model through SD simulation software, such
as STELLA, DYNAMO.
3. Testing : Verifying and Validating the SD model.
4, Implementation : Analyzing the model according to decision scenarios,
Conventionally, the causal feedback relationship among elements must be represented in mathematical
form, such as C=A+B. In addition, such relationship should be completely certain. That is, while we say
C=A+B, B is always equal to A+C exactly at all cases.
Necessity for Integration
However, when the real world problems occur the following three conditions, the conventional SD
methodology may not be met.
1. Some elements can not be quantified by numeric index, for example, “industry level". Usually, we deal
with such question by using artificial index to quantify and thus represent this sort of elements. For
example, we define closed interval (0, 1] to represent the industry level, 0 lowest and 1 highest. From
that definition, however, the operation should be done with much care and the interpretation of
simulation outcome is more unnatural relative to the real world problems. Therefore, we should allow
the linguistic representation for such elements, like "low", "medium", and “high” for industry level.
2. The relationship among elements sometimes, but practically, may not be all certain. For instance,
perhaps some cases hold, B=A+C, but in some other conditions, B=D+C. Although some SD software,
like STELLA, DYNAMO, provide such IF..THEN feature, more sophisticted IF..THEN relationship
can not be represented yet.
3. Furthermore, we are not often sure about the relationship among elements. Perhaps we have only 80%
certain about B+A+C, and 60% about B=D+C. It should be noted that B now has two values with
different certainty at the mean time. SD does not serve that also.
To provide the preceeding three features, we utilize the Expert Systems aid developed in detail at
the following two sections. As a problem solving tool, ES provides flexible knowledge representation,
including: numeric and linguistic forms, as well as IF..THEN structure specified in rule based ES.
Moreover, the reasoning mechanism of ES allows the inexact conditions, as known as inexact reasoning,
Therefore, we first introduce the integration framework, and then describe how to integrate SD and ES in
detail.
Framework and References of Expert Systems Aid to System Dynamics
From Figure 1 to Figure 4, we show the integration framework and relative references of ES aid to SD.
Note that the framework is based on SD modeling process introduced above. Our efforts will focus on the
Fig.2, formulation stage in the following sections. In that, 2, 3, 4, 5 items will be discussed more detailly.
Conceptualization Formulation .
Expert Systems Aids} Relative References Expert Systems Aids | Relative References
1. Convert causal
1. Extract knowledge| Kienhans,é ..1986, | | diagram to SD lsaiewrioastresy
about problems | 1989) flow chart ee 1990) »
‘(Metern Peter,1986) Sas
(Camara, & ..., 1986) 2. Represent relations
(Young, 1985) fa aerae form (Meter, 1986,87,89)
a eo Be 3. Use fuzzy theory | (Milling, 1988)
4, Multidit ional
3. Provide models to| (Banerjee, & ....1990) Saale Cane tes 220
users after request 5. Allo ertait rs
4, Use expertise to | (Merten, 1989 ) eT. | Qa 988)
analyze patterns
Fig. 1 Integrated reference of conceptualization Fig.2 Formulation
Testing Implementation
Expert Systems Aids | Relative References Expert Systems Aids | Relative References
1 ue expertise to | (Sue Shau-Yi, 1987) | 1. Use ree (Sue Shau-Yi, 1987)
alidation exp!
Fig.3 Testing Fig.4 Impirmentation
Integration of System Dynamics and Rule Based Reasoning Mechanism
Rule based reasoning mechanism plays an important role in rule based ES. It represents knowledge in
tule form, such as IF..THEN, and deals with uncertainty through certainty factor or fuzzy reasoning
features. Section 3.1 to 3.3 will prove how to integrate three properties of rule based reasoning into SD
models,
Rule Based Reasoning
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Th eS
: Bg
co
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In addition to conventional SD knowledge representation, direct, mathematical form, we now add the rule
form to represent the relationship of elements. In perspective of Programming Language, we just utilize the
logic operator AND, OR, NOT, and decisive construct IF..THEN .. ELSE, and nested-if features.
In fact, DYNAMO has already provided such IF..THEN feature through its CLIP function. For example,
A=CLIP(, 1.5P, R, S) means IF R>=S THEN A=P, ELSE A=1,5P. Such CLIP function has been used in
(Metern Peter, 1986] to describe the structural change in SD models. However, the conventional CLIP
function can not describe the following sophisticated nested-ifs.
IF R>=S THEN A=P,
ELSE IF U>V THEN A=P+Q,
ELSE A=P+R.
Note that A=B+C is just another form of IF <true> THEN A=B+C, which means the generality of rule
form representation.
Multidimensional Simulation
Multidimentional simulation [Camara, A., Antunes, P., Pinheiro, M. and Seixas, M., 1987] means in
the simulation process, the number of elements’ data type is more than only one, numeric type. That is, in
addition to conventional numeric data type, it is allowed to have linguistic (or even others) data type. In this
paper, for those elements difficult to be quantified in nature, we can represent and measure them in
linguistic data type.
In SD models, we say “human's memory is effected by his age”. Owing to the difficulty and unnature to
quantify the "memory" and “age”, we let memory be represented by “good”, "medium", and “poor", and also
quantify age by " young", "medium", and "old". Naturally, we say that the larger the age, the worse the
memory. Thus coupling with the rule form, we say
IF age="old" THEN memory="poor",
ELSE IF age="medium" THEN memory="medium",
ELSE IF age="young" THEN memory="good".
That is so intutive that we do not need to quantify "age" and "memory" with care any more.
Dealing with Uncertatinty
ES usually utilizes certainty factor or fuzzy reasoning techniques to solve. uncertainty. Here we choose
certainty factor [Guru Reference Manual, 1985] as our integration solution into SD models.
First, we define [0, 1] closed interval as our certainty boundary. When we say A=2B+C CF 80 means
that we have 80% certainty about A=2B+C. "CF" is abbreviation of “Certainty Factor."
Combining with IF..THEN structure, we say
IF A>B THEN C=2P+Q CF 80,
ELSE C=2P+0.5Q CF 60.
Notice that the sum of these two certainty factors is not equal to 100. That means certainty factor is a
kind of possibility, not probabilty.
As above example, C has only one value 2P+Q or 2P+0.5Q. Another practical example, however, is as
follows.
IF A> B THEN C=2P+Q CF 80,
ELSE C=2P+0.5Q CF 80,
C=2P+0.5R CF 60.
Here, if A<B, C gets two values, 2P+0.5Q and 2P+0,5R, at a time. Such variable C is known as a fuzzy
variable. .
If there is a fuzzy variable in a SD model, it will be propagated to other variables through operation, and
thus slow down the simulation performance. Therefore, while practical implementation, we need an
effective mechanism to control the expansion of fuzziness. [Negoita, Constantin V., 1985] [Guru Reference
Manual, 1985]
Feature Summary after Integration
As far, we integrate three properties of rule based reasoning mechanism into SD models.
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1, Represent the relationship among elements by IF..THEN..ELSE structure.
2. Add linguistic data type in addition to conventional numeric form.
3. Utilize certainty factor to deal with uncertainty, and thus allow the usage of fuzzy variable.
After such integration, we can make some breakthrough to solve quantification and uncertainty problems
in conventional SD models.
Modification of System Dynamics Modeling Tools
Building theoretical bases as above, we now start to modify the modeling tools of conventional SD in
order to adopt the intregration features into the whole modeling process.
Modifying Causal Diagram
According to the following Fig.5, there are six catagories to modify the causal diagram.
IF .. THEN
F Yes
a No | structure | structure
a changed | not changed
z {Yes} 1 2 3 Fig.5 Modified classification
Y|No| 4 5 6 of cansal diagram
1. If there is no IF..THEN ‘and fuzzy variable, every symbol remains the same as the conventional causal
diagram,
2. If there occurs IF.. THEN, but model structure is not changed, and no fuzzy variable, as below,
IF C<U THEN A=2D+E,
ELSE A=2D+1.5E.
We may represent it by the following symbols in Fig.6.
i A ~#u
+ ie
a As [0 >,
‘i ,
Ay
é aN aw
Se =
SN Fig.7
‘It means that A has two possible values under two different conditions which are both positively effected by
Dand E. Since C and U occur in IF part, there are no positive or negative symbols to A. The representation
is analogous when the number of possible conditions is more than two.
3. If IF.. THEN occurs, and structure is changed, but no fuzzy variable, for instance,
IF U>D THEN A=2D+E,
ELSE A=2F-E.
Symbols will be as Fig.7 above.
‘That means in one case, A is positively effected by D and E, but in the other, A is positively effected by F
and negatively by E. The representation is analogous when the number of possible conditions is more than
two.
4. There is no IF.. THEN, but fuzzy variable exists. For example,
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A=2D+E CF 60
A=2D+1.5E CF 80
can be represented by the following Fig.8.
+ A
+ A 1H) +
oe
a4 + a /
0] B (2]-
2}
“Sl ~ aw
Ty if’ d <
Fig.8 Fig.9
Here, A has two values meanwhile, both positively effected by D and E. Or as below,
A=2D+E CF 60
A=2F-E CF 80
can be depicted as Fig.9.
Here A also has two values meanwhile, but one positively effected by D and E, the other positively effected
by F and negatively by E. The representation is analogous when the number of possible conditions is more
than two.
5. IF.. THEN and fuzzy variables occur, but no structural change, as the following.
IF B>U THEN A=2D+E,
Fig.10
ELSE A=2D+15E CF 60,
A=2D+1.7E CF 80.
It can be pictured as Fig.10 below.
(1) and (2) say that there are two conditions by IF..THEN, and [1] and [2] represent there are two values at a
time in both (1) and (2) conditions. The representation is analogous when the number of possible
conditions is more than two.
6. IF..THEN, fuzzy variables, and structural change all occur. For example,
IF U="medium" THEN A=2D+E,
ELSE A=2F+E CF 60,
A=2G+E CF 80.
may be Fig.11.
= TAGs
It means that in the first IF..THEN case, A is positively effected by D and E, but in the other, A has two
values at a time, one value positively effected by D and E, another also positively effected by E and G. Note
that U is a linguistic variable, and is located in IF part, so there are no positive or negative signs from U to
A. The representation is analogous when the number of possible conditions is more than two.
Adding Element Specification Table
After integrating rule based reasoning mechanism, the causal diagram contains so much modeling
information that we need another tool, as data dictionary in information systems analysis stage, to carry
information about each element in a SD model.
Therefore, we add a tool named "element specification table" to describe the followings of each element.
1. Identity number : specification of each element.
2. Name : full name and abbreviation used in the causal diagram.
3. Range : data type and its range for possible values if it has.
4. Description : about element's relationship relative to others in natural language or standrized pseudocode
5. Minimal confidence degree : degree to represent the minimal acceptable certainty factor respective to each
element. That is, if the element's certainty factor is smaller than this minimal confidence degree, we
cancel the value in such fuzzy variable. This item is available to control the expansion of fuzzy
variables. 4
6. Note : other information available to simulation.
The format of element specification table could be as Fig.12.
ID.
Note Fig.12 Format of Element
Specification Table
Modifying System Dynamics Diagram
In SD Diagram, we choose levels, rates, physical flows, information flows, sources, sinks, auxiliary
variables, parameters, and necessary delays in the model.
As our modification in causal diagram, the same will be used on SD diagram.
Considerations of Coding Tools
It's time for us to consider the coding tools to implement SD models. Here, we discuss three classes for
integrated SD models theoretically.
1, Based on SD software, we may couple with othér software tools to fulfill rule based reasoning features,
The followings are four coupling choices.
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Se.
-- No coupling : for example, we use DYNAMO to complete the whole integrated features. [Metern Peter,
P., 1986] utilizes CLIP and SWITCH function to implement simple IF..THEN feature, but loss of
uncertainty.
-- Coupling with 3GL : to illustarte, we may implement rule based reasoning in FORTRAN, as well as
DYNAMO interface funtions.
-- Coupling with ES language : using PROLOG or LISP for rule based reasoning, we make DYNAMO as
interface with them,
-- Coupling with package software : for instance, use LOTUS 1-2-3 and DYNAMO for integration.
2. Based on ES shell or ES language, we may implement rule based reasoning easily. However, many SD
features may not be achieved by ES tools. This class of technique may take much effort. There are two.
possible couplings.
-- Implement only by ES shell or ES language, for example, GURU [Uhran, J., Ghiaseddin, N. and
Bualuan, R., 1988], and PROLOG [Camara, A., Antunes, P., Pinheiro, M. and Seixas, M., 1987].
-- Coupling with 3GL : for example, C and PROLOG for SD features and rule based reasoning
respectively.
3. New integrated software, we suggest, for implementation. We can fulfill the preceeding integrated
features only by another new software tool. Nevertheless, it is unnecessary to design in the whole new
source codes. Perhaps we may utilize ithe framework of SD software, say STELLA, and then just add
integrated features and accompanied user interfaces.
Prototype for Integration
In this section, we demonstarte an example based on the theories in the preceeding two sections. This
example origins from the chapter 9 model of [Peterson, S., Richmond, B., and Vescuso, P., 1987]. we
modify it to show the integrated features described above. The followings are consistent with the four-stage
SD modeling process. The causal diagram shows as the following Fig.13.
custom_fraction net_flow _
a aS ue as
°) —Per_day
re a
birth_fraction
ae
consumption CD li nm, production
Fig.13 Intergrate causal diagram of prototype
Note that “births” is determined under three different conditions. One is positively effected. by
“pirth_fraction"; another is positively effected by "birth_fraction" and “custom_fraction"; the other is
positively effected by "birth_fraction" and negatively effected by "custom_fraction". We may see "custom"
appears at IF part. Moreover, "Food" is here a fuzzy variable with two values meanwhile. Both are
positively effected by "production" and negatively by “consumption”.
After the causal diagram, we should complete element specification table for each element. Here we
provide two instances, “Food” - Fig. 14, "births" - Fig. 15. Then the SD diagram is as Fig. 16. "Custom"
is a linguistic variable. We now represent the relationship more naturally through IF..THEN mechanism.
Fuzzy variable "Food" carries two values with 60 and 80 certainty factor respectively.
Coded and compiled by TURBO C version 2.0, we show the simulation outcomes as Fig. 17.
D. 1
Name } Food
Range | Numerical type, Fuzzy variable
Food=Food+DT*(production-consumption)*0.95
Description CF 80
Food=Food+DT*(production-consumption) CF 80
Minimal 50
Confidence
Degree
Note.
Fig.14
ID. 3
Name births (birth rate)
Range Numerical type
IF custom="normal birth rate” THEN
births = Population*birth_fraction
Description ELSE IF custom="high birth rate" THEN
births = Population*(birth_fraction+custom_fraction),
ELSE IF custom="Iow birth rate” THEN
births = Population*(birth_fraction-custom_fraction)
Minimal
Confidence 50
Degree
Note Fig.15
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2) Ol
consumption production
Fig.16 System Dynamics Diagram of Prototyping Integrated
Note that in "food_per_capita", the value of fuzzy variable "Food" is the sum average of
multiplication of its values and respective certainty factor weight. This is an effective
method to control the expansion of fuzzy variables while simulation.
——t— Population
Fig.17 Integrated Implementation of Prototyping
Conclusion
Integrating IF..THEN representation, linguistic data type, and certainty factor into conventional
SD models, we make SD more powerful to solve practical problems.
As future research, we will first accent the development of the new integration software. In
addition, various and wide applications of integrated features and detailed discussion about implemention
techniques, such as inexact reasoning in SD environment, will be as much our research interest.
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