Dear Peter and list members, Perhaps not _all_ members of this audience are as eminent as you may think - I for one am just a random hack, who occasionally jumps into the debate while trying not to embarrass myself too badly.
What I say below is largely based on ignorance and presumably contains statements which are simply wrong. It reflects some of my current perceptions on fuzzy theory and is an attempt to clarify its philosophical position - I'm hoping the experts will correct me where I go wrong. > I have asked this group whether the theory of fuzzy sets or the cognate > theory of rough sets rests on an ontology that asserts the "reality" of > "surface" phenomena. But so far (apparently) no one thinks my question makes > enough sense to warrant even an attempt at an answer. Yes, I would also like to know the answer to that one. I am not a fuzzy theorist, but my guess is that the answer is "no". Here's my motivation: First, I am assuming that "surface phenomena" refers to what Prof Zadeh calls "perceptions", and that by "reality" you mean "objective reality" (as opposed to a relativistic view where every person can have his/her own subjective reality). Suppose we are told that John is tall. Now, does this "perception" (I assume the word perception is meant to refer to a perception in the mind of the author of the statement "John is tall") have an objective meaning in the fuzzy set framework? I.e. if we define a fuzzy set of tall people and assign John a degree of membership to this set based on the above statement, is this assignment a necessary consequence of the statement (i.e. the perception has objective reality), or is there a many-to-many mapping between the perception and the fuzzy set membership we assign (i.e. perception is not fully defined in its own right and requires interpretation - it has no objective reality). My current understanding of fuzzy theory is that it adopts the latter position - perceptions are defined to be subjective. Presumably one reason for choosing to work with the concept of perceptions is that this means we do not need to assume any objective reality and can work in a relativistic framework instead. Unfortunately this also allows us to state problems without having to define exactly what we mean, because different people are to be allowed different interpretations of the problem. Thus we have problems that are considered admissable, although we cannot ask whether their proposed solutions are "correct", whether some solutions are better than others, or whether there is an optimal solution. > The other possible explanation I see for the occasional efficacy of fuzzy > logic in the management of information conveyed by perceptions and other > such things is Explanation starts here: > a background assumption (a necessary background assumption?) > that the evolution and survival of the human species have led human beings > to have thoughts and sorting mechanisms that _somehow_ work and that, > therefore -- if one wishes to advance human understanding of the world -- it > makes sense for human beings to try to figure out how their now-innate > concepts manage to work as well as they do in the cosmos that human beings > inhabit. End of explanation. > I wonder if this alternative possible explanation for the efficacy > of fuzzy thinking is as meaningless to this audience as was my conjecture > that an ontology of surfaces underlies fuzzy logic. Perhaps you left out a paragraph in the explanation? I mean, the whole explanation didn't even mention fuzzy thinking once. What is the link between fuzzy thinking and the issues you mention in the explanation? > I suppose one possible answer to all of my questions is that fuzzy logic is > a poor stepchild to answers framed by the standard probability calculus, > which are the answers we will get if and when we study nature carefully > enough and long enough. (But, then, what should we do and how should we > think "in the meantime"?) I'm not sure that fuzzy theorists would like that characterisation - I always thought that fuzzy theory is claimed to be a more accurate description of the world than can be obtained using bivalent logic, not just a crude approximation to a more accurate bivalent logic based description. regards, Konrad
