**Previous message:**Chiraz Latiri Cherif: "order relation"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

*>I see your difficulty. You think that if A is a fuzzy term, and its
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*>membership function is denoted simply by a, let's say, then the
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*>one-minus rule of negation gives the membership function of NOT A as
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*>1-a. Hence the "middle" is included, so to speak, and LEM and LC
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*>should fail, as indeed it obviously does if the min-max rules are then
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*>applied. For we have A AND NOT A being modeled in the meta-language as
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*>min(a,1-a), which gives us the well-known middle with a peak at 0.5
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*>(assuming of course that a has its max at 1, its min at 0, and there
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*>is gradation in-between).
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*>Now let's try another rule of conjunction, in particular the
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*>Lukasiewicz bounded-sum rule, for which we have for two membership
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*>functions a and b, and their corresponding terms A and B,
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*> mu[A AND B] = a AND b = max(0, a+b-1).
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*>In the particular case where B is NOT A, and b=1-a, we have under this
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*>rule
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*> a AND b = max(0,a+1-a-1) = 0 everywhere
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*>and in accordance with the law of contradiction, the term A AND NOT A
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*>is rendered as the comstant absurdity whose membership value is
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*>everywhere 0. LC is upheld.
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I am employed at the Silesian Technical University as a university teacher.

In my work I have to very often answer to the following question.

"Does John know topic x?"

or

"What is the relation between topic x and Mr John's knowledge?"

Sometimes it is very difficult to answer this question.

In order to answer to this question I use number between 2 and 5.

If John know topic x, then I use number 5.

If John don't know topic x, I use number 2.

If I am not sure that John know topic x, I use number between 2 and 5.

I think that this is a definition of fuzzy set.

For example.

John belong to the set of people which know topic x with degree 4=

= John get 4 at the class test.

Let's us consider the following situation?

John get 3 at the class test. ( m(John | Topic x)=3)

Marry get 4 at the class test. ( m(Marry | Topic x)=4)

Do John and Mary know topic x?

What is the answer to this question?

a) m(John and Marry | Topic x)=min{3, 4}=3

b) m(John and Marry | Topic x)=(3+4)/2 (I think that this is quite good

solution.)

c) m(John and Marry | Topic x)=max(2, 3+4-5)= 2 (I think this is cruel.)

What is the correct answer?

Andrzej Pownuk

P.S.

I belong to the set of people

who know English language

with degree of membership 3=.

I apologise for that.

------------------------------------------------

MSc. Andrzej Pownuk

Chair of Theoretical Mechanics

Silesian University of Technology

E-mail: pownuk@zeus.polsl.gliwice.pl

URL: http://zeus.polsl.gliwice.pl/~pownuk

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**Next message:**Wise: "Re Fuzzy and Datamining"**Previous message:**Chiraz Latiri Cherif: "order relation"**Maybe in reply to:**Joe Pfeiffer: "Thomas' Fuzziness and Probability"**Next in thread:**Herman Rubin: "Re: Thomas' Fuzziness and Probability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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