fuzzy logic

Alexis Read ucapare@ucl.ac.uk
Tue May 28 07:50:02 2002

On Mon, 27 May 2002, jeremy wrote:

> [was: the logic of the infinite]
> --- Kyle wrote:
> I think you are thinking/imagining at too high a level.  No useful
> conclusions can be made when you are not bounded by the mess we call
> reality of computing.
> ---
> Then I'll step down a notch. :)   I will leave aside all notions of subjectivity (and the Infinite), as computer systems are only able to deal with users' behaviour, not the users themselves.
> --- Alexis:
> It is very neccessary though, to be able to view the different
> levels of abstraction depending on the user's needs.
> ---
> OK. So let's say our user needs to abstract the human heartbeat, say for a biofeedback device. Are we primarily concerned with the user's needs -- abstracting a harmonic, analog, cyclical, highly variable event -- or with our computer system's need for granular division of time and information into byte-sized equal segments? The two needs -- those of the user and those of the computer/programmer -- are relatively opposed in this case. Whose needs take precedence?

As I recall, the human heartbeat behaves chaotically ie. it can be
modelled reletively accurately by a simple equation like:

z=sin(z^2 + c) where z=p+iq (comple number)

(not actually the eq., but this is chaotic ie. complex,
almost random behavior arises from normal equations)

Note there is no computing here, just math modelling. The equation
sin(theta) is 'analog' as theta is infinitely variable.
For building a biofeedback device you'd be concerned with connecting your
input and feedback (output) to this equation (algorithm), so you could
model this in the OS as an asynchronous process, or with boundary conditions
as needed. The computing hardware WILL present a problem after this as
currently there are few asynchronous devices around, and the input will be
quantised ie. analog-digital. The important thing is that the OS is not the
'bottleneck' and the granularity of the I/O can be scaled.

Basically, the computing aspect is abstracted from the model.

> In other words, is an OS to be judged primarily by its ability to abstract computer hardware or real-world events? Is this basically the same as the distinction between the LLL and the HLL? What possibilities are there for reconciling the two (digital and analog information, right- and left-brain activity)?

ONE way of looking at the LLL, HLL division could be that the HLL
abstracts the computing aspect, and the LLL provides computing
asbstraction eg. hardware abstraction, OO, etc.

Note the above is a mathamatical example, but it is possible to do
modelling on non mathematical things eg. properties of objects (type
conformance etc.).
Even if you cannot model the whole of a system, you can still reason about
the behaviour of the hidden aspects of a model.

The hardware interface between real world data and the computer will for
the near future be granular, with the grain size dictated by the
application need. Modelling ie. anything inside the OS, CAN be 'analog'

So, I guess the answer you're looking for is 'the judge of an OS is
whether it can abstract the computing aspect.'
Reasoning about real-world events is possible to a limited extent, that
which is bounded by logic and physics.

> Can this kind of conflict be addressed by fuzzy logic? To what extent is fuzzy logic relevant to a Tunes-like system?

Not that relevant in my opinion.

The concept of Fuzzy Logic (FL) was conceived by Lotfi Zadeh, a professor
at the University of California at Berkley, and presented not as a control
methodology, but as a way of processing data by allowing partial set
membership rather than crisp set membership or non-membership.

FL incorporates a simple, rule-based IF X AND Y THEN Z approach to a
solving control problem rather than attempting to model a system
mathematically. The FL model is empirically-based, relying on an
operator's experience rather than their technical understanding of the
system. For
example, rather than dealing with temperature control in terms such as "SP
=500F", "T <1000F", or "210C <TEMP <220C", terms like "IF (process
is too cool) AND (process is getting colder) THEN (add heat to the

http://www.seattlerobotics.org/encoder/mar98/fuz/fl_part1.html#WHAT IS

Notice the hardware still is discrete!

Rewrite logic can encompass fuzzy logic, and that's all i'd be interested
in to start with. Its important to get the foundations right, and look at
what amount to subgroups later.

> questions, questions, questions...

The truth is out there!

Alexis Read
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