**Subject: **Fuzzy Logic vs. System Dynamics

**From: **Bradd Libby (*bradd@wpi.edu*)

**Date: **Fri Aug 18 2000 - 13:15:27 MET DST

**sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**artfldodgr@my-deja.com: "Bart "Fuzzy Thinker" Kosko"**Previous message:**Robin B. Lake: "Re: Fuzzy matches between XML entities ?"**Next in thread:**Paul Victor Birke: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Paul Victor Birke: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Bradd Libby: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Bradd Libby: "Re: Fuzzy Logic vs. System Dynamics"

I am familiar with both Fuzzy Logic and System Dynamics, a methodology

developed in the late 1950's at MIT for studying complex systems, though I

do not claim to be an expert in either. (For those readers unfamiliar

with SD, I'd recommend visiting http://sysdyn.mit.edu/ and many of the

links from that site, for basic background information.)

Someone familiar with Fuzzy Logic reading about System Dynamics (or

conversely, in my case, someone familiar with System Dynamics reading

about Fuzzy Logic) will notice that the two disciplines share many

important features:

Like Fuzzy Logic, System Dynamics is often concerned with the

comprehension/control of complex systems (that is, systems containing

multiple parts interacting according to nonlinear relationships; systems

where not necessarily all of the variables are known, quantifiable, and

easily measured; systems prone to 'non-intuitive' and sometimes 'chaotic'

behavior). For Fuzzy Logic, the applications seem to be more

'engineering' oriented (control of a cement kiln, a subway system, an

inverted pendulum), for System Dynamics more 'management' oriented (urban

dynamics, limits to economic growth, business simulations), but the

underlying principles of feedback, information delays, uncertain

quantities and the like remain similar.

And the similarity, both in function and in notation, between what fuzzy

logicians call 'cognitive maps' and system dynamicists 'causal loop

diagrams' is so striking that I can say with relative confidence that they

must be the cross-application of one idea - If they have been developed in

parallel without reference to each other, then their visual and functional

similarity would be a truly dramatic coincidence.

It seems to me that any methodology that promises its practitioners a

legitimate ability to analyze, understand, and control complex, dynamic,

non-intuitive systems must offer three things (though the names I've

selected are a bit trite, I admit):

* First, a methodology (Fuzzy Logic, System Dynamics, or some other)

must have a "MINDSET": call it a 'paradigm', 'worldview', 'Welt-

anschauung', what have you, the methodology must offer some way

of viewing a given system that is different from what a non-

practitioner would employ (and that this mindset greatly clarifies

and simplifies the study of the system).

It seems to me that both Fuzzy Logic and System Dynamics offer

legitimate mindsets: For Fuzzy Logic the operative maxims are a

rejection of IF-THEN/EITHER-OR/BLACK-WHITE in favor of probability

distributions and continuous functions; for System Dynamics they are

what Dr. Richmond (founder of High Performance Systems,

www.hps-inc.com) calls 'The 7 Systems Thinking Skills' (to name a

few: change-over-time thinking, system-as-cause thinking,

closed-feedback-loop thinking). But both methodologies offer a

mindset.

* Second, the methodology must have a "TOOLSET": that is, it must

give its user some 'ready to use' techniques for applying the

mindset in the real world. For System Dynamics this toolset is the

'stock-and-flow language' (a visual means of describing complex

systems as 'states' (what engineers call 'state variables') and

'rates' (the rate of change of these variables)), causal loop

diagrams, so-called 'table functions' (essentially, fuzzy functions),

behavior archetypes (including 'shifting the burden' and the

'addiction' cycle). State space diagrams (graphing two or three

system variables on a coordinate system) are also popular.

By 'toolset' I would like to emphasize that I am NOT refering to

specific software packages. The 'toolset' I'm refering to consists

of the _techniques_ employed or fostered by a given software

tool. By analogy: Microsoft Word is _not_ a toolset - written

alphabet (along with vocabulary and grammar) is a toolset and

Microsoft Word is a software package designed to facilitate

implementing those tools. In System Dynamics, ithink/STELLA

is not a toolset - stock-and-flow mapping is a tool and ithink/STELLA

is a software package designed to facilitate the implementation of

that tool.

The toolset of Fuzzy Logic, it seems to me (and please correct me if

I am wrong or incomplete), consists of 'fuzzy cognitive maps' (an

analog to 'causal loop diagrams'), fuzzy function diagrams (typically

depicted as overlapping triangles (or other shapes) along a given

axis; the classic example being a temperature axis with triangles

overlapping for 'very cold', 'cold', 'normal', 'hot', 'very hot'),

and defuzzifying algorithms.

* Third, the methodology must provide an 'INSTRUCTION SET': not

necessarily a true instruction set of the sort one receives with

a 'some assembly required' toy, a hard-and-fast 'paint by the

numbers' algorithm, but at the very least a guide for how the

mindset and toolset should be employed.

For System Dynamics the instruction set is the 'modeling

method' (analogous to the scientific method): observe, model, test,

repeat; building complexity and 'robustness' with each iteration,

though trying to keep the model as simple as possible. (In many

ways, it shares qualities with coding in C++ or any other programming

language.)

In these respects, then, System Dynamics is a 'complete package,' whereas

Fuzzy Logic, it seems, consists primarily of a mindset. Fuzzy function

diagrams, fuzzy cognitive maps, and defuzzifying algorithms combined (and

please correct me if I'm wrong) represent at best half of a toolset: they

offer a partial solution, but fail in some key respects. In the Fuzzy

Future, Bart Kosko describes how the triangular shape of fuzzy functions

is not always the best solution, but that sometimes other shapes are

employed. But Fuzzy Logic remains silent on how to determine the best

shape and therefore fuzzy logicians are forced to resort to trial-and-

error, evolutionary algorithms, or any other tools/techniques they have at

their disposal to solve this problem. Additionally, Fuzzy Logic says

little about the identification of important (critical) system variables.

For sufficiently complex systems, these are not trivial matters. And as

far as an instruction set is concerned, Fuzzy Logic seems to say 'Your on

your own.' The practitioner is left alone to decide whether the best

implementation should be in the form of a software program, a hardwired

circuit, or some other means, and to decide the way of implementing the

Fuggy Logic mindset.

I'm speculating here, but perhaps that reason that Fuzzy Logic has been so

sucessfully empoloyed in the areas it has been is because the majority of

its pracititioners to date have been engineers, logicians, and the

generally mathematically inclined, who have been employing engineering

principles (such as, start simple and add complexity) and the scientific

method implicitly, and mathematical and engineering analytical methods

explicitly, to compensate for those areas where Fuzzy Logic remains...

unsupportive.

I have several questions that I would like to pose to those who are more

knowledgeable and experienced in Fuzzy Logic than I, but I think they all

boil down to one central issue: What does Fuzzy Logic offer that System

Dynamics lacks?

That is, why shouldn't Fuzzy Logic be subsumed as a subset of System

Dynamics, or should it? Given the choice between System Dynamics and

Fuzzy Logic for solving a complex control problem, why wouldn't one

immediately choose the former without further consideration, confident

that, in the worst-case scenario, any solution that can be devised in

Fuzzy Logic can be implemented using table functions in a System Dynamics

simulation software application? In short, what justification is there

for Fuzzy Logic to be considered a separate discipline?

I look forward to hearing your thoughts on this matter and to having any

misperceptions I may have of either Fuzzy Logic or System Dynamics hastily

corrected.

Best regards,

Bradd Libby.

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**Next message:**artfldodgr@my-deja.com: "Bart "Fuzzy Thinker" Kosko"**Previous message:**Robin B. Lake: "Re: Fuzzy matches between XML entities ?"**Next in thread:**Paul Victor Birke: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Paul Victor Birke: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Bradd Libby: "Re: Fuzzy Logic vs. System Dynamics"**Reply:**Bradd Libby: "Re: Fuzzy Logic vs. System Dynamics"

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