What is a fuzzy rule?

[Bill Silvert]

I have been working with decision support tools based on fuzzy logic
for many years, but recently I have been told by several
mathematicians that the rules I am using have nothing to do with fuzzy
logic. I am baffled by this and hope that someone can tell me whether
there has been a drastic divergence in the definition of fuzzy
concepts and what these people are thinking of.

The kinds of rules I am using are like those in standard demos, such
as for buying a house:
IF the house is close to work AND not too expensive THEN ...
where one can obtain crisp rules by defining "close to work" and "too
expensive" in terms of precise distances and prices, but in practical
terms these are fuzzy concepts and thus a house that is a little too
far from work might be acceptable if the price is very low (the actual
rules under debate deal with issues such as nutrient levels). What is
the basis for saying that this kind of rule has nothing to do with
fuzzy logic?

[Walter Banks]

Bill

They are splitting hairs. Fuzzy logic is the math behind
multivalued logic where logical states are a range of values
between and including 0 and 1.

( Boolean logic is a subset of multivalued rules)

Fuzzy logic rules are a series of competing logical
expressions that are used for decision making. They
are evaluated using fuzzy logic to select the best outcome.

Regards,

Walter..


--
Walter Banks
Byte Craft Limited
http://www.bytecraft.com
***@bytecraft.com

.

Post by Bill Silvert
I have been working with decision support tools based on fuzzy logic
for many years, but recently I have been told by several
mathematicians that the rules I am using have nothing to do with fuzzy
logic. I am baffled by this and hope that someone can tell me whether
there has been a drastic divergence in the definition of fuzzy
concepts and what these people are thinking of.
The kinds of rules I am using are like those in standard demos, such
IF the house is close to work AND not too expensive THEN ...
where one can obtain crisp rules by defining "close to work" and "too
expensive" in terms of precise distances and prices, but in practical
terms these are fuzzy concepts and thus a house that is a little too
far from work might be acceptable if the price is very low (the actual
rules under debate deal with issues such as nutrient levels). What is
the basis for saying that this kind of rule has nothing to do with
fuzzy logic?

[Joe Pfeiffer]

Post by Bill Silvert
I have been working with decision support tools based on fuzzy logic
for many years, but recently I have been told by several
mathematicians that the rules I am using have nothing to do with fuzzy
logic. I am baffled by this and hope that someone can tell me whether
there has been a drastic divergence in the definition of fuzzy
concepts and what these people are thinking of.
The kinds of rules I am using are like those in standard demos, such
IF the house is close to work AND not too expensive THEN ...
where one can obtain crisp rules by defining "close to work" and "too
expensive" in terms of precise distances and prices, but in practical
terms these are fuzzy concepts and thus a house that is a little too
far from work might be acceptable if the price is very low (the actual
rules under debate deal with issues such as nutrient levels). What is
the basis for saying that this kind of rule has nothing to do with
fuzzy logic?

Your description doesn't quite give me a clear idea of how your rules
work -- when you say you can obtain crisp rules by defining "close to
work" it sounds like you're using a boolean value. But then your
description of "too far OK if cheap enough" it goes back to sounding
fuzzy.

So... if your idea of "close to work" has a value of 0 at 1.5 miles
away or farther, and a value of 1 at .5 miles away or closer, and is
something in between (for instance, a linear function) in between the
two distances, you've got a fuzzy rule and I've got no idea what the
mathemeticians are talking about.

If your idea of "close to work" is 0 at distances beyond one mile, and 1
for distances at or within one mile, it's crisp.

[Dmitry A. Kazakov]

Post by Joe Pfeiffer

Post by Bill Silvert
I have been working with decision support tools based on fuzzy logic
for many years, but recently I have been told by several
mathematicians that the rules I am using have nothing to do with fuzzy
logic. I am baffled by this and hope that someone can tell me whether
there has been a drastic divergence in the definition of fuzzy
concepts and what these people are thinking of.
The kinds of rules I am using are like those in standard demos, such
IF the house is close to work AND not too expensive THEN ...
where one can obtain crisp rules by defining "close to work" and "too
expensive" in terms of precise distances and prices, but in practical
terms these are fuzzy concepts and thus a house that is a little too
far from work might be acceptable if the price is very low (the actual
rules under debate deal with issues such as nutrient levels). What is
the basis for saying that this kind of rule has nothing to do with
fuzzy logic?

Your description doesn't quite give me a clear idea of how your rules
work -- when you say you can obtain crisp rules by defining "close to
work" it sounds like you're using a boolean value. But then your
description of "too far OK if cheap enough" it goes back to sounding
fuzzy.
So... if your idea of "close to work" has a value of 0 at 1.5 miles
away or farther, and a value of 1 at .5 miles away or closer, and is
something in between (for instance, a linear function) in between the
two distances, you've got a fuzzy rule and I've got no idea what the
mathemeticians are talking about.
If your idea of "close to work" is 0 at distances beyond one mile, and 1
for distances at or within one mile, it's crisp.

There could be another source of uncertainty. The function "close to work"
may be crisp but if the argument "distance" is not, the "value" of the
function will be a distribution of truth values over distances.

---
I cannot tell for mathematicians mentioned by OP, but to me any fuzzy
concept shall include an interpretation of rules/operations etc. In
particular the meaning of truth values, which tells why the numeric result
is like it is. The problem with ad-hoc rules used by some people is that
they do not care about giving any interpretation that would justify the
result obtained.

To give an example, let us consider the theory of probability. The meaning
of "truth value" there is the probability, a set measure. All statistical
rules can be tacked down to the probabilities. This justifies the numeric
results and gives the premises of use.

Similarly if we take fuzzy set theory, the only way I see as a
mathematician, is to postulate some set measure and consistently apply it
in order to get rules of inference, composition etc. The
possibility/necessity is kind of such measure.

[Silvert]

Post by Joe Pfeiffer
Your description doesn't quite give me a clear idea of how your rules
work -- when you say you can obtain crisp rules by defining "close to
work" it sounds like you're using a boolean value.  But then your
description of "too far OK if cheap enough" it goes back to sounding
fuzzy.
So...  if your idea of "close to work" has a value of 0 at 1.5 miles
away or farther, and a value of 1 at .5 miles away or closer, and is
something in between (for instance, a linear function) in between the
two distances, you've got a fuzzy rule and I've got no idea what the
mathemeticians are talking about.
If your idea of "close to work" is 0 at distances beyond one mile, and 1
for distances at or within one mile, it's crisp.

Sorry, I thought that concepts like "close to work" were so obviously
fuzzy that I didn't specify the membership. Up to 500 m the membership
is 1, over 50 km the membership is 0, and there is some sort of
interpolation in between. Just think of what the words mean in human
terms.

[Joe Pfeiffer]

Post by Silvert

Post by Joe Pfeiffer
Your description doesn't quite give me a clear idea of how your rules
work -- when you say you can obtain crisp rules by defining "close to
work" it sounds like you're using a boolean value.  But then your
description of "too far OK if cheap enough" it goes back to sounding
fuzzy.
So...  if your idea of "close to work" has a value of 0 at 1.5 miles
away or farther, and a value of 1 at .5 miles away or closer, and is
something in between (for instance, a linear function) in between the
two distances, you've got a fuzzy rule and I've got no idea what the
mathemeticians are talking about.
If your idea of "close to work" is 0 at distances beyond one mile, and 1
for distances at or within one mile, it's crisp.

Sorry, I thought that concepts like "close to work" were so obviously
fuzzy that I didn't specify the membership. Up to 500 m the membership
is 1, over 50 km the membership is 0, and there is some sort of
interpolation in between. Just think of what the words mean in human
terms.

I'd have agreed, except that you then went on to say it gave you a crisp
rule. As I've seen the term used, "crisp" means boolean which is why I
was confused. With your clarification, I'm back to having no idea what
their objection was.