- Interesting, but not true.

Membership functions are not obtained by statistical sampling. They are

subjective interpretations. Fuzzy logic is based on a foundation of

linguistic variables. Most fuzzy logic models are remarkably tolerant of

differing subjective interpretations, as they are intended to be.

A membership function does not equate to a pdf. There is absolutely no

requirement that its integral equal 1.

Allan

At 02:23 PM 9/8/2000, Martin Sewell wrote:>

>Allan Kaminsky wrote:

> >Equating fuzzy logic to probability is a common fallacy among those

> >unfamiliar with fuzzy logic. Any of the standard introductory texts (Kosko

> >or Cox are representative authors) refute this "urban legend."

>

>news:comp.ai.fuzzy FAQ: "What is the relationship between fuzzy truth

>values and probabilities?"

>http://www.cs.cmu.edu/Web/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-10.html

>

>My own comments:

>In fuzzy theory, if we say that a man is tall with a degree

>of membership of 0.8, we don't mean that he is tall 80% of the time.

>

>But how can we justify using the figure 0.8? Where did it come

>from? We could ask a random sample of people to define their

>interpretation of (say) short, average and tall. If the man is 6' tall

>and it transpires that 80% of the sample consider this to be tall, we

>could also argue that if we ask a person at random, the probability that

>they consider 6' as belonging to the set 'tall' is 0.8.

>

>This is a standard example of the use of fuzzy theory and is intended to

>show that the fuzzy membership function can be interpreted as a probability

>density function (pdf) in the limiting case where the area under the

>membership functions equals one.

>

>

>To unsubscribe from this group, send an email to:

>Behavioral-Finance-unsubscribe@egroups.com - An interesting web-site, with statistical software links, on fuzzy clustering is maintained by Frank Hoppner at:
**http://www.fuzzy-clustering.de/**Fuzzy clustering is related to but not identical to fuzzy logic.

Dick MarchAllan Kaminsky wrote:

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---------------------------------------------------------------------_->Interesting, but not true.

Membership functions are not obtained by statistical sampling. They are

subjective interpretations. Fuzzy logic is based on a foundation of

linguistic variables. Most fuzzy logic models are remarkably tolerant of

differing subjective interpretations, as they are intended to be.A membership function does not equate to a pdf. There is absolutely no

requirement that its integral equal 1.Allan

At 02:23 PM 9/8/2000, Martin Sewell wrote:

>

>Allan Kaminsky wrote:

> >Equating fuzzy logic to probability is a common fallacy among those

> >unfamiliar with fuzzy logic. Any of the standard introductory texts (Kosko

> >or Cox are representative authors) refute this "urban legend."

>

>news:comp.ai.fuzzy FAQ: "What is the relationship between fuzzy truth

>values and probabilities?"

>http://www.cs.cmu.edu/Web/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-10.html

>

>My own comments:

>In fuzzy theory, if we say that a man is tall with a degree

>of membership of 0.8, we don't mean that he is tall 80% of the time.

>

>But how can we justify using the figure 0.8? Where did it come

>from? We could ask a random sample of people to define their

>interpretation of (say) short, average and tall. If the man is 6' tall

>and it transpires that 80% of the sample consider this to be tall, we

>could also argue that if we ask a person at random, the probability that

>they consider 6' as belonging to the set 'tall' is 0.8.

>

>This is a standard example of the use of fuzzy theory and is intended to

>show that the fuzzy membership function can be interpreted as a probability

>density function (pdf) in the limiting case where the area under the

>membership functions equals one.

>

>

>To unsubscribe from this group, send an email to:

>Behavioral-Finance-unsubscribe@egroups.comTo unsubscribe from this group, send an email to:

Behavioral-Finance-unsubscribe@egroups.com On Friday, September 08, 2000, 10:50:58 AM, you wrote:

MS> Okay, sorry - the two paragraphs above are unrelated.

Aha - I didn't get that from the read.

MS> The first quote is my own (I'm a fuzzy cynic).

I'm beginning to get that message, though :-).

MS> In the interests of balance and information dissemination, I also provided

MS> the link to the news:comp.ai.fuzzy FAQ as a 'definitive' guide to all

MS> things fuzzy.

MS> As you can imagine, they're unlikely to dismiss fuzzy logic in the way that

MS> I do!

You're absolutely right on that one :-).

Thanks for the clarification,

ztrader- Allan Kaminsky wrote:
>Interesting, but not true.

news:comp.ai.fuzzy FAQ: "How are membership values determined?"

>

>Membership functions are not obtained by statistical sampling. They are

>subjective interpretations. Fuzzy logic is based on a foundation of

>linguistic variables. Most fuzzy logic models are remarkably tolerant of

>differing subjective interpretations, as they are intended to be.

>

>A membership function does not equate to a pdf. There is absolutely no

>requirement that its integral equal 1.

http://www.cs.cmu.edu/Web/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-9.html

My comments:

Often the shapes and ranges of the fuzzy membership functions are

defined by a human expert. The human expert has built up his knowledge

from experience of past events, which is, in effect, statistical

inference. For example, if we employ an 'expert' trader to set the fuzzy

membership functions for an upward move and a downward move in a market, he

is really using his prior knowledge of historical price movements. If, in

his experience, the market has risen 7 times out of 10 given a particular

price pattern, he will incorporate this knowledge into the fuzzy membership

functions. Whether the area under his membership functions equates to one,

or otherwise is simply a matter of scaling, and therefore irrelevant.

Remember that fuzzy membership values *can* also be determined with

probability densities in mind (all probability distributions are fuzzy sets.)

The very fact that there are so many ways (an infinite number), and that

there is so little objective reasoning when it comes to defining fuzzy

membership functions is one of the inherent weaknesses of fuzzy logic.