Predictor said:
"I think the usual criticisms of fuzzy logic revolve around an assumption that fuzzy logical truth values are equivalent to probability, which I think is a dubious assumption."
I couldn't agree more. This is the heart of the matter.
The term "uncertainty" can be used in many ways. In statistics, uncertainty can be quantified as the standard deviation of the sampling distribution. If you want to reduce uncertainty, you collect more data.
However, in philosophy uncertainty can refer to conceptual uncertainty. For example, what is a "proposition?" 'The cat is on the mat' is a proposition. 'If you heat water to 100 degrees Celsius, it will boil' is a proposition.
But what about: 'If Eisenhower had failed in the Normandy invasion, Hitler would have won the war.'
Is THAT a proposition? It certainly has the FORM of one. Unfortunately, there is no clear rule. Counterfactual conditionals are a fuzzy case. We are UNCERTAIN whether it is a proposition or not. To the point: our uncertainty would not be mitigated by gathering more information. We already have all the information that is possible to have. Our uncertainty is conceptual.
Fuzzy logic, it seems to me, is useful for this kind of conceptual uncertainty. If we wanted to simulate an economic system, one might state a rule: if the economy goes into recession, then lower interest rates. Well, what if GDP does not actually stall, but instead grows sluggish and fails to respond to the usual economic stimuli. Are we in a recession? who knows. We want to say: "well the point is, it sure SEEMS like a recession, so let's call it a recession and solve the problem," at which point the rule kicks in.
Similarly in a control system: the engine is technically not overheating, but it is running very hot and the RPM's are getting fast (what is "fast"?)... therefore we invoke the rule to slow down the RPMs.
In short, statistical methods are useful when uncertainty is related to probability. i.e., when there IS a fact of the matter, but sampling error prevents us from seeing it clearly so we minimize our error (through maximum likelihood, sample size, etc).
In contrast, fuzzy logic is useful when uncertainty is conceptual, i.e. when there is NOT neccessarily a fact of the matter (except maybe by arbitrary conventions), so we must loosen our criteria so that our rule system mirrors our experience of the real world (e.g. well we are PROBABLY in a recession, or the engine is PROBABLY stressed, or a counterfactual conditional is SOMEWHAT like a proposition).
The philosophical points I made are based on Wittgenstein's analysis of ordinary language (Philosophical Investigations), which provides what I think is an outstanding basis for Fuzzy Logic.
