Gene Kofman (its@icanect.net)
Sat, 18 Oct 1997 06:10:25 +0100
Doug wrote:
> I made an inference from what you said above: formal logic is a SPoV
> invention of the SOM-types. Do you agree?
Yes, Boolean (yes/no) logic separates everything into sets with crisp
boundaries the same way SOM does. This simplification of everyday reality
is useful in many cases, but very artificial. It does not allow to simulate
an expert, who very often makes decisions without being able to formalize
them into a crisp yes/no tree.
> I also infer that fuzzy logic is more MoQ-like. Is that what you are
> hinting?
I do feel similarities. Of course, Fuzzy logic is just one of the patterns
in the MoQ structure. I'd like to be able to define the similarities, but
not sure how important that is. I look at the Fuzzy logic mostly from
engeneering point of view (I use it in my programs), but I originaly was
attracted to it on a higher level by its 'many truths' possibilities.
> If so, then could we use a kind of fuzzy representation of the four
> levels and their contexts, relationships, etc.?
I think we already did, when LS writes about interdependency and mutual
mediation of levels. It seems to me that level boundaries are not crisp,
they overlap. For example, it's very difficult to pinpoint were inorganic
stops and bio begins.
> As I understand it, fuzzy logic is still not continuous, it has
> multiple, settable discrete levels instead of the formal dichotomies and
> trichotomies, right?
Sets in Fuzzy logic overlap, they are continuous. Degree of overlap is
'context' specific.
Let's say, we wanted to separate all people into two sets of 'tall' and
'short'. According to the Boolean logic we would establish a threshold,
let's say 6 feet. In that case, a 5'9'' person and 6' person would belong
to the two completely different sets, despite the fact that we all
understand that they are pretty close in height. Expert system based on
Boolean logic would trigger two different rules to handle these two people.
According to the Fuzzy logic, we would create two overlapping sets: 'short'
from 0' to 6' and 'tall' from 3' to 9'. Each person would belong to both of
these sets with a different degree of membership: 4'6'' person would be
'short' to a degree of .5 and 'tall' to a degree of .5, 5'9'' person would
be 'short' to a degree of .03 and 'tall' to a degree of .97, 6' person
would be 'short' to a degree of 0 and 'tall' to a degree of 1. These
numbers (.97 and 1) reflect closeness in height of 5'9'' and 6' persons.
Fuzzy logic based expert system would trigger several rules to a different
degree, based on the each person's membership functions. In this case,
5'9'' and 6' persons would be treated very similarly.
Gene.
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