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Martine De Cock <Martine.DeCock@rug.ac.be> writes:

*> Cristian Fabbi wrote:
*

*>>
*

*>> studied by FL? Why do we say that with Fuzzy Logic we will make
*

*>> computers thinking like human?
*

*>
*

*> Because we believe "that humans deal with imprecision and uncertainty
*

*> by using linguistic values and that they apply some kind of approximate
*

*> reasoning techniques rather than exact numerical values and first order
*

*> logic". (Fuzzy Sets and Approximate Reasoning, Etienne E. Kerre, Xian
*

*> Jiaotong University Press, Xian (P.R. China), 1999).
*

It does not follow that because humans "deal with imprecision and uncertainty"

they must therefore be using the specific mathematical formalism called

``fuzzy logic'' to do so, or that machines using this mathematical formalism

will ``think'' exactly the same way humans think. Many different forms of

approximate, qualitative, and probabilistic reasoning methods have been

proposed in the literature; there is no evidence that the human reasoning

process uses _ANY_ of them.

Moreover, Cox's Theorem [Cox, R.T.: ``Probability, frequency, and

reasonable expectation,'' Am. J. Phys. v.14, pp.1--13 (1946)] proves

conclusively that =ALL= possible approximate reasoning methods other than

Bayesian Probability Theory fail to be logically self-consistent in some

way or other --- and that includes fuzzy logic. Hence, if any method of

approximate reasoning is to be preferred, it would have to be Bayesian

reasoning. (This is =NOT= to say that _humans_ use Bayesian reasoning,

but only that _if_ we wish our machines to think in a way compatible with

logic, Bayesian reasoning has been mathematically proved to be the =ONLY=

approximate reasoning method that is capable of doing so. Any other method

--- including Fuzzy Logic --- will necessarily yield logical paradoxes

and inconsistencies under certain circumstances.)

-- Gordon D. Pusch

perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'

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