Fuzzy Logic and System Dynamics Models

[marco@idsia.ch (Marco Wiering)]

I am a PhD student Artificial Intelligence, and
study different modeling approaches. I like system
dynamics for its clarity, although I think that
system dynamics might profit from combining their
models with those in Artificial Intelligence.

I would describe system dynamics as numerical
expert systems. There are a bunch of diff. eq.
instead of if-then rules, since the models have
to work mostly with numbers and less with logic,
but for the other parts there are lots of similarities.
(Search for generic models, knowledge-engineering etc).

Expert systems can use fuzzy logic for modeling
the confidence in observations, rules and commonly
use some simple combination rules which receive
all confidence-measures (of rules, and observations)
and use those to assign a confidence to the product.
Fuzzy systems can use a large deal of collected
statistics, and are able to map fuzzy-sets to
fuzzy-sets in this way. These statistics might be
found by Machine Learning, i.e. by performing statistical
analysis on large data-sets.

The common ground of system dynamics and fuzzy logic
is that both use structures numerical representations.

The difference is that fuzzy logic take large sets as
a single observations by using probability densities
over this observation. This would correspond to performing
monte-carlo simulations with system dynamics with some
small noise in the diff. eqs. The fuzzy systems usually
need a lot of storage-space and knowledge, the system
dynamics models would use more time and less storage-space
(when they use monte-carlo simulations).

The difference between time and space is that you cannot
reuse time.
M. Furst

Marco Wiering
IDSIA
marco@idsia.ch
http://www.idsia.ch

[jnoble2@mmm.com]

Id like to pose a modeling question to the system dynamics community
on this list. My exposure to systems thinking / system dynamics has
been in business school and some of Peter Senges work. I can see
valuable contributions these philosophies / techniques could
contribute to my own manufacturing organization. One of the
recurring points in the S.D. literature is the use of mental knowledge
and "models" of interviewees working in the system as a primary source
of information for building S.D. models. I was wondering about the
application of fuzzy logic techniques to capture these policies and
decision processes.

Fuzzy logics strength is at quantifying the qualitative intuition and
heuristics used in real-world situations where crisp data and
categories are lacking. Also, it allows non-linear relationships to
be captured in membership functions that are accessible to the
non-mathematical manager and more intuitive than differential
equations. These strengths would seem to make the technique helpful
in facilitating the policy model-building process. The tool has been
used extensively in industrial and commercial product control problems
but would seem to apply to managerial and organizational "control"
problems as well.

I am not an expert in either system dynamics or fuzzy logic, but my
question to the members of the list is in two parts:

- Has fuzzy logic or other expert system techniques been
incorporated into system dynamic models for policy modeling research?

- Are there currently any commercial packages that accomplish this?

Your feedback would be appreciated.

Jon Noble
3M Mfg. Planning Systems
jnoble2@mmm.com

["Dr. Michael J. Radzicki"]

To Jon Noble:

See: Bjornar Tessem and Pal Davidsens article titled: "Fuzzy System
Dynamics: An Approach to Vague and Qualitative Variables in Simulation."
System Dynamics Review 10(1): 49-62.

Peace.

Mike

Dr. Michael J. Radzicki
Associate Professor of Economics
Department of Social Science & Policy Studies
Worcester Polytechnic Institute
Worcester, Massachusetts 01609-2280
United States of America
(508) 831-5767 (Voice)
(508) 831-5896 (Fax)
mjradz@wpi.edu (Email)

[jimhines@interserv.com]

In a way our models output IS fuzzy logic, in the following sense. In all
SD models the output is numbers. In many (though not all!) cases the numbers
are interpretted in a logical sense, rather than in a precise-number sense.
So, to describe the output wed say "high", "low", "growing", etc. We are
concerned about whether the output belongs to, say, the "high" class of
output. The higher the numbers, the more the output belongs to the
"high" class. Similarly with "growing", "declining", "collapsing",
"oscillating", etc.

Regards,

Jim Hines
LeapTec and M.I.T.
JimHines@Interserv.Com

["C. Thomas Higgins"]

I am not quite sure what Jims point is "In a way our models output IS =
fuzzy logic". The remainder of the response seems to draw a parallel =
between the results of SD modeling and Fuzzy Logic. Are these then =
mutually exclusive as descriptive language? Are they the same thing =
growing up under different labels?

I am not a formal student, teacher or professional of SD, Fuzzy Logic, =
Systems Thinking etc. Nor a mathematician. I follow these disciplines =
because they enchant me. The only thing I am even remotely sure about =
is that all these things have one character in common. They are all =
arbitrary linguistic distinctions addressing the elusive real world. =
However, being arbitrary does not in any way trivialize the journey to =
understand what is real. We must start somewhere.

In my own thinking SD perhaps intersects with a set called Fuzzy Logic. =
Perhaps to clear my thinking the participants could provide me with =
examples of what is SD but not Fuzzy Logic and what is Fuzzy Logic but =
not SD. While we are at it maybe somethings that are both SD and Fuzzy =
Logic.

>From Bart Koskos Fuzzy Thinking:

So far as the laws of mathematics refer to reality, they are not =
certain.
And so far as they are certain, they do not refer to reality.

Albert Einstien


Tom Higgins
loscann@pacific.telebyte.co

["Klehe, Joachim (jxklehe)"]

To: system-dynamics@facteur.std.com
Subject: RE: QUERY Fuzzy Logic and System Dynamics Models (SD0495)

Jon, you wrote:
* - Are there currently any commercial packages that accomplish this?

Reply: You may want to investigate "Fuzzy Logic for the Management of
Uncertainty" by Zadeh & Kocprzyk, also look into McNeills and Thros
implementation of Bart Koskos Fuzzy Cognitive Maps in their WinTel
based program Fuzzy Thought Amplifier. Contact McNeill at Fuzzy Systems
engineering (619) 748-7384, or get their book, "Fuzzy Logic: A Practical
Approach" ISBN: 0-12-485965-8 which includes a crippled version of the
software.

Joe Klehe
(jxklehe@pacbell.com)