Rich Ulrich <wpilib@pitt.edu> wrote in message news:<o4elntgdqdr1vb0gvtt7ng3leeraqp723m@4ax.com>...> On Wed, 15 Aug 2001 05:50:46 GMT, "Earl Cox" <earldcox1@home.com> > wrote:
(( cuts ))> > Smithson's book gave me the impression of disparate > researchers, different models of "fuzzy logic," and a field > that was not unified to any great extent. A decade > later, is that different?
Earl certainly refers to "fuzzy logic" in a way that would disregard what I and other researchers have contributed. Where all fuzzy researchers necessarily agree is that there exist terms in natural language with membership or characteristic function over a relevant domain such that some points in the domain have membership strictly between 0 and 1: there are degrees of membership. That is what fuzziness means. And that is where agreement pretty much ends. For the very basic concept of what operationally is this notion of degree of membership, and how to measure it, there is disagreement. And indeed, that is what started this thread. I take the view that fuzzy membership is really a form of semantic likelihood, a notion which explains in pretty straightforward terms what fuzziness is (st least in natural language semantics), and how it arises, given that even in calibrational settings, there is randomness in usage. The next point of disagreement relates to the choice of rules for connectives. Earl appears to champion the min-max rules. And the fact that these rules fail to obey law of excluded middle (LEM), and law of contradiction (LC) is trumpeted often as a virtue, and it is implied that fuzziness in itself *requires* that LEM and LC must fail. Here again, I for one disagree. I maintain that natural language fuzziness is not sufficient to cause LEM and LC to fail. For example, the term "tall" everyone would agree is fuzzy in the sense earlier described. But no witness would testify that her attacker was "tall and not tall" without inviting the derision of the court, and the fuzziness of the term will not come to her rescue. I conclude that LC holds in natural language even for fuzzy terms. Clearly, Earl has a different take on the matter, but I have been pointing out this simple thought experiment for a long time now, and I have encountered not a word in response from anyone suggesting I am wrong. Fuzziness does not failure of LEM or LC entail. Moreover, I and other researchers have shown how, within a fuzzy set theory, purely as a matter of uninterpreted mathematics, LEM and LC may be upheld.> Does fuzzy logic have to be *very* carefully tailored > to a particular problem?
This is not a point of principle. All models are "wrong" by their very nature. Some, however, are useful. So the goodness of a model is never an absolute, there are always other considerations that enter, economy for one. So I would not attack "fuzzy logic" from this angle. Instead, like Wittgenstein, I seek the "logical clarification of thoughts", and I apply the same attitude to Bayes, for example, and to classical stats, both of which can be useful, even when philosophical foundations are far from settled. Regards, S. F. Thomas