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• ## Re[2]: [Behavioral-Finance] Fuzzy models : a question

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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
Message 1 of 12 , Sep 8, 2000
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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
>
>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
Message 2 of 12 , Sep 8, 2000
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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 March

Allan 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
>
>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

To 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
Message 3 of 12 , Sep 8, 2000
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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,

• ... news:comp.ai.fuzzy FAQ: How are membership values determined? http://www.cs.cmu.edu/Web/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-9.html My comments:
Message 4 of 12 , Sep 8, 2000
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Allan Kaminsky wrote:
>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.

news:comp.ai.fuzzy FAQ: "How are membership values determined?"
http://www.cs.cmu.edu/Web/Groups/AI/html/faqs/ai/fuzzy/part1/faq-doc-9.html

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.
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