This is precisely what fuzzy systems are all about. Notice, for example, how
the natural linguistics are instrinsically fuzzy themselves ... there's
nothing exact about the word "precisely"! It is also true that precise
measurements are artificial. If anything, there is a cost associated with
increasing precision or crispness, which was clearly observed in Zadeh's
1973 IEEE SMC paper. The most direct example, of course, is the rapidly
increasing word-length for a digital computer to represent increasingly
precise real numbers.
Each subsystem, artificial, natural or hybrid has it's own internal
precision limiting bound. Practically, even this bound is often not reached
or really used. For a simple semi-numerical example, consider an important
measurement in the chemical process industries - one of measuring and
inferring the success of an acid/base type of neutralisation process ...
from high school chemistry we know that "perfectly neutral" has a pH = 7.0.
The extreme precision limit could be, say, the sensor with |error| < 0.05.
However, for the true process downstream it does not care as long as the
|true error| < 0.2, say. Then the hidden cost of excess precision is clear
and economic: the entire process control system sort of exponentially zooms
up in cost for every order of magnitude in precision (close to the truth).
Finding the "optimal" configuration ... it's all in the soft heuristics of
an error variable that ranges from -0.2 to +0.2. It's also a severely
nonlinear process. In fact, even the crisp controllers are gain-scheduled
for this. Fuzzy methods appear just right here for measurement and control.
The broadly qualitative equation is
heuristics + crisp logic = fuzzy logic
Very informally, one can also use quasi-quantum mechanics, particularly
Heisenberg's uncertainty principle:
dx * dp >= Ksys
where dx is the precision error, and dp some relevant energy-cost function,
price, and Ksys is system-specific. It could also be viewed as a crude model
for an appropriate version of Goedel's Incompleteness Theorem - which really
puts a "universal limitation spanner" into crisp logic and its mathematical
Fairly clearly, fuzzy logic is a little more than somewhat natural.
From: Wise <firstname.lastname@example.org>
To: Multiple recipients of list <email@example.com>
Date: Monday, May 21, 2001 7:33 PM
Subject: Re: "Inevitable Illusions"
>I nursed for a while and we often needed to dip
>a plastic stick, containing a number of chemically impregnated
>pieces of paper up the length of the stick, into a urine sample.
>These sticks gave us an indication of sugar, proteins, etc found in
>the urine sample. Inevitably they were graded not just true or false
>In real life the diagnosis and treatment of disease is not just true or
>Your example talks about an absoluteness in having a disease which is
>inevitably not always the case.
>We can have a person who can belong to the fuzzy set of diabetics who we
>of as having diabetic tendencies. In fuzzy terms they have a small
>in the diabetic set.
>The classical logic would have us render them as diabetic or not diabetic.
>preciseness is actually a dangerous circumstance because now we have to
>not treat. Real life actually uses fuzzy logical strategies to handle these
>people and their
>A full on, full blown diabetic (a real life description) is someone who, in
>terms, has a high membership value in the diabetic set.
>The words (descriptions) are optional, the fuzzy math under the bonnet is
>I think that a lot of discomfort with fuzziness is its ability to
>accommodate the superficial, the changing
>and very malleable language layer. They are only descriptors used to label
>both the sets and then the
>extent of membership in those sets.
>As descriptors ....slightly diabetic, less diabetic, diabetic tendencies
>allows me and
>you to put our heads at the lower end of the spectrum (low membership
>values) of diabetic types.
>We do need to be on the same page with respect to our fuzzy set
>our fuzzy value universe,
>etc... if we jointly intend doing any thing more precise, but often to hold
>a conceptual conversation
>a lot of this stuff is just not required, it is implied.
>If I tendered the following advise
> to treat your diabetic tendencies patient with diet and review
>after a while
>without a lot of definitions, to prop up the words tendencies and review
>the word while you would get the drift of
>what I recommended.
>Now if you wanted to meter out a precise dose of chemical A for particular
>Diabetic lets talk about the
>membership value of that person in the diabetic set and then using fuzzy
>mathematics calculate the
>dose and frequency of chemical A.
>Fuzzy control systems work today that achieve this type of precision.
>And that my friend is TRUE in a fuzzy kind of way.
>Chris De Voir wrote in message ...
>>> -----Original Message-----
>>> From: firstname.lastname@example.org
>>> [mailto:email@example.com]On Behalf Of Wise
>>> Sent: Wednesday, May 16, 2001 6:31 PM
>>> To: Multiple recipients of list
>>> Subject: Re: "Inevitable Illusions"
>>My question is: Supposing that all the data in the above example take on
>>Fuzzy values, how does one maintain logical clarity of Bayes to make good
>>predictions/decisions using Fuzzy still subject to limited rationality?
>>Regardless, the answer may still be, no, this has not been studied. But
>>thanks for the response.
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