Re: Fuzzy Logic vs. System Dynamics


Subject: Re: Fuzzy Logic vs. System Dynamics
From: Bradd Libby (bradd@wpi.edu)
Date: Tue Aug 22 2000 - 04:14:14 MET DST


================================================

Bradd Libby, bradd@wpi.edu, writes:
>
> For Fuzzy Logic, the applications seem to be more 'engineering'
> oriented (control of a cement kiln, a subway system, an inverted
> pendulum)...

William Siler replies:
>
> Alas, altogether too many people, including many of the fuzzy systems
> crew, have this idea, although it is usually not put forward so
> explicitly. Earl Cox's work in the business field (see one of his
> several books) is certainly non-engineering, and our own recent work has
> been in decision making in a hospital intensive care unit. Unfortunately
> the success of fuzzy systems theory in process control has led to a
> preoccupation with this field to the virtual exclusion of work in
> non-control applications.

I hope that I didn't imply that 'engineering problems' were the exclusive
domain of Fuzzy Logic and 'business problems' the domain of System
Dynamics. My main point was that Fuzzy Logic's historical sucesses (to
date) have been 'hard' control problems, while System Dynamic's successes
have been in the area of 'soft' systems analysis (An important sidenote,
though, is that Forrester orignally dubbed System Dynamics 'Industrial
Dynamics,' as he saw its value primarily in areas like supply chain
management, inventory control, logistics/operations research, and the
like, but changed to 'System Dynamics' when he realized, with the help of
a former mayor of Boston, that it could be applied far beyond the
factory.). Indeed, based on the close parallels I've observed between the
two disciplines, it seems to me that any system that can be modelled with
System Dynamics can be handled by Fuzzy Logic as well, and vice-versa
(which of the two is 'more appropriate' for a given problem, easier to
apply, or more intuitive is most likely at the discretion of the
practitioner), which leads me to wonder why we consider them to be
separate disciplines.

I think perhaps a distinction between the two disciplines more interesting
than the 'engineering' vs. 'business' applications is my observation that,
and perhaps this is wrong, System Dynamics is typically employed to
_analyze_ or _understand_ 'problematic' behavior in complex systems (in
fact, some system dynamicists have seriously considered re-renaming their
field 'Problem Dynamics'), while Fuzzy Logic is typically employed to
_control_ or _correct_ problematic behavior. Perhaps the distinction is
academic (Why build understanding if not to correct the problem...and
conversely, how can you correct the problem if you don't understand it?),
but nevertheless, the chief practitioners in these respective fields seem
to have "sold" their disciplines to the Unacquainted in these terms.

It's interesting to hear that you are applying Fuzzy Logic to medical
care, as one of the early applications of System Dynamics to business
simulation was a multiplayer board game called 'Friday Night at the E.R.'
(www.blearning.com) - and this is certainly not the only application of
System Dyanmics to this field.

========================================

Bradd Libby, bradd@wpi.edu, writes:

> > For Fuzzy Logic the operative maxims are a
> > rejection of IF-THEN/EITHER-OR/BLACK-WHITE in favor of probability
> > distributions and continuous functions;

Bob Briggs replies:
>
> A couple of quick points off the top of my head...your observation above
> isn't entirely accurate. Fuzzy logicians don't reject if-then (if one does,
> I'd like to hear the argument). FL applications need an inference engine,
> and I use if-then rules all the time as I set up relationships between fuzzy
> variables without feeling polluted. Better to say that fuzzy logic rejects
> bivalence.

I agree and disagree (How's that for bivalence for ya'?):

Yes, I agree that my selection of terms was sloppy - I think that just
saying 'BLACK-WHITE' would have conveyed what I intended. (Perhaps
tossing the words 'Boolean' or 'binary' in there somewhere would have
helped as well.) The IF-THEN I had in mind was more along the lines of
absolute causality (A drinking glass falling of the table is a problem
(i.e, IF (position-of-glass) is off the table, THEN problem exists), and
one standing in the center is not a problem (i.e, IF (position-of-glass)
is not off the table, THEN problem does not exist). Boolean logic states
that a glass 90% of the way to the edge is also not a problem (i.e., IF
(position-of-glass) is near edge of table, THEN problem does not exist),
while Fuzzy Logic rejects this sharp distinction.

And No, I disagree that 'Fuzzy logicians don't reject if-then' - I think
that they do (and furthermore, that for most applications, it's good that
they do, and they should continue to do so). I realize that fuzzy
relationships are typically phrased in IF-THEN terms (e.g., 'IF
(position-of-glass) is (far-from-center-of-table) THEN
(push-glass-hard-to-center-of-table)'), but when one rejects Boolean
values (0 or 1) in favor of a continuum of values between 0 and 1,
inclusive, then any IF-THEN statements that are generated containing fuzzy
variables become mathematically equivalent to normalized (and, often,
non-linear) functions.

In other words, there is no difference between my previous example:

IF (position-of-glass) is (far-from-the-center-of-the-table) THEN
(push-glass-hard-to-center-of-table)')

and,

F = q * Dx

where F is the amount of force to be applied in the direction of the
center of the table, Dx is the distance that separates the glass from the
center, and 'q' is a proportionality constant. (I realize my engineering
background is showing in my terminology, but basically this relation says:
'As the position of the glass gets further from the center of the table,
increase the force that's pushing in the direction of the center.') The
two statements are conceptually identical.

If 'q' is a variable (perhaps one that depends on Dx), then the force
curve could be made to assume any desired (linear or nonlinear) shape -
even a triangle. (Preferably, this expression would be such that the force
appraches infinity as the glass approaches the edge, thus ensuring that
the glass would not fall off the table (assuming that the glass doesn't
shatter!).)

So, while fuzzy logicians may retain the IF-THEN *terminology* in applying
Fuzzy Logic, they are actually applying continuous functions, and thereby
rejecting the 'IF A exists/happens, THEN B exists/happens' mindset.

 
> I'd be interested to know more about the sets that are used under the system
> dynamics umbrella. Forrester invented magnetic core RAM. Pretty bivalent
> stuff, eh? Does that same bivalence carry through to the math? (This not
> asked very well, but I hope the folks on this list understand what I'm trying
> to convey.)

The System Dynamics language (the 'stock and flow' language) has no formal
means of representing IF-THEN statements, although all of the simulation
software packages available, to the best of my knowledge, have added on
the ability to use IF, THEN, OR, NOT, ELSE operators. System dynamicists
tend to disfavor the use of these operators, reserving them only for when
it is much more convenient to use them than to not use them. (In fact,
'Continuous Thinking,' a preference for continuous functions over absolute
causality IF-THEN statements is another of the 7 Systems Thinking skills
identified by Dr. Barry Richmond (who received his Ph.D. in System
Dynamics under Dr. Forrester at MIT).

The reasons for rejecting Boolean logic in System Dynamics models are the
same as for rejecting them in Fuzzy Logic models - they can cause
erroneous results and undesired behavior. Case in point: H. Van Dyke
Parunak, whose work on agent-based systems was mentioned in the cover
article, called 'Ant-based Optimatization' (or something similar), of the
March 2000 issue of Scientific American, and Rick Riolo, an ithink/STELLA
user and professor at U Michigan who is a member of the BACH group (whose
members include John Holland (the 'H'), the inventor of evolutionary
algorithms, and Robert Axelrod (the 'A'), the author of _The Evolution of
Cooperation_ and _The Complexity of Cooperation_), co-authored a project
called DASCh (Dynamic Analysis of Supply Chains), some of the
papers/presentations for which can be found on the web at
www.erim.org/cec/sce.htm and www.erim.org/cec/projects/dasch.htm.

In their project, Dr.s Parunak and Riolo modelled a production-
distribution system and found interesting (read: chaotic) behavior in a
very simple mathematical model. The model is detailed in their reports
"Dynamic Analysis of Supply Chains" and "Agent-Based Modeling vs.
Equation-Based Modeling", which are available at the second URL listed
above. I found it interesting that chaotic behavior was seen in such a
simple model, but was dismayed to discover that the cause of the behavior
was an unruly IF-THEN statement of the form:

IF (x is less than some critical value called x#) THEN (y = 0) ELSE (y =
some large positive value called N)

The problem was that x depended on y, so that if x evaluated above the
critical value, then y became equal to N, causing x to fall, causing y to
become equal to 0, causing x to rise above the critical value again. In
other words, the chaotic behavior results from the discontinuity in the
equation for y, and subsequently the behavior of the system depends on the
time increment selected for the simulating the system over time (a
hallmark that the behavior is an artifact of the formulation of the
equations, rather than true chaos).

When this IF-THEN statement is replaced by a 'fuzzy function' of
the form:

IF (x is less than some critical value called x#) THEN (y = (x/x#)*N) ELSE
(y = N)

(In other words, y is 90% of N when x is 90% of x#, and y is N when x is
greater than or equal to x#), when this substitution is made, all of the
chaotic behavior of the system disappears, and most of the analysis based
on the supposed chaotic behavior is invalidated.

Thus the dangers of Boolean logic and of rejecting Continuous Thinking.

Best regards,
Bradd Libby.

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