# Re: Thomas' Fuzziness and Probability

From: Herman Rubin (hrubin@odds.stat.purdue.edu)
Date: Sat Aug 18 2001 - 09:45:30 MET DST

• Next message: WSiler@aol.com: "Re: Thomas' Fuzziness and Probability"

In article <9l818o\$36a\$4@fbi-news.cs.uni-dortmund.de>,
Stephan Lehmke <Stephan.Lehmke@cs.uni-dortmund.de> wrote:
>In article <23af61c2.0108122107.6f0e7aab@posting.google.com>, Robert Dodier writes:

>> Consider the mayor of Ashtabula. Let A = "mayor's right eye is blue".
>> Let B = "mayor's left eye is blue". Let B' = "mayor's left eye is brown".
>> What do you suppose is the truth value of A B ? What about A B' ?

>Maybe I'm missing something here.

>Could you again, with rigorous logical notation, state this problem,
>and point out the difference with two-valued logic?

>> The difficulty is that rules of the kind applied in fuzzy logic
>> ignore relations between the elements of a compound proposition.

It does not give any problems, looked at carefully.

Probability is NOT a truth value system, and does not
pretend to be so. In a truth value system, the truth
of a compound proposition follows from that of the
simple propositions involved. Probabilities have to
be exist for all compounds simultaneously. If one
starts with the fuzzy idea and adds this, probability
is what will result.

```--
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
hrubin@stat.purdue.edu         Phone: (765)494-6054   FAX: (765)494-0558
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