Joe Pfeiffer wrote:> > (hmmm, I'm seeing responses to posts by Thomas, but not his posts themselves) > Stephan.Lehmke@cs.uni-dortmund.de (Stephan Lehmke) writes: > >> In article <3B674E1D.F47314AF@verizon.net>, S. F. Thomas writes: >> >> * Furthermore, according to Zadeh, Fuzzyness should be used to >> `compress' knowledge representation, in terms of the number of >> concepts, rules, ... used. So I expect to be able to evaluate the >> color of an orange entirely by comparing its membership degree in the >> fuzzy sets of red, green, and blue objects, without having to employ a >> plethora of auxilliary concepts like "reddish" , "somewhat red", >> "orange red", etc. pp. > > Right -- it seems like ``reddish orange'' ought to mean a high > membership in orange, and a non-zero membership in red.
It is an entirely empirical question, and it seems to me that the point in issue can be adequately addressed using the device of the calibrational proposition with a binary response variable.>>>> For empirically finding a membership degree, I'd rather have people >>>> mark the `degree of tallness' on a continuous scale between `tall' and >>>> `not tall at all' and take the average. >>> >>> I don't like it, because your subjects still have to be >>> told what it is you mean by "degree of tallness". Which is a kind of >>> circular question-begging in my opinion. > > Actually, it seems to me that your use of calibrational propositions > answers this quite nicely. If you ask, ``on a scale of 0 to 10, to > what extent would you say Tom is tall'' then what you get back as an > average is a notion of how people assign the membership function, > without ever having to produce an actual definition of tallness for > them to use.
But why do you need a scale of 0 to 10. When we *use* fuzzy terms, the utterances of which they form part are whole utterances; they do not come in degrees. The terms may be profusely hedged, and we have a plethora of hedge terms such as "somewhat", "more or less", "broadly", etc. that can be pressed into service when necessary. But at the end of the day, the utterances in which they are used are whole utterances, not utterances to a degree. Thus it seems to me the proper calibrational question to ask is whether the subject in question would herself use the term (possibly hedged) in question to describe the exemplar in question, on the attribute in question. Asking the subject to give a degree response amounts to asking the subject to estimate the degree of membership directly. Clearly we all have the ability to do that, ie. effectively to step into the meta-language and to express our prior views as to how the population at large actually uses a fuzzy term. That though should not blind us to the underlying point of principle, which is that uncertainty, in actual use, of a term, is a binary issue: utterances, however hedged, come whole, not in degrees.> -- > Joseph J. Pfeiffer, Jr., Ph.D. Phone -- (505) 646-1605 > Department of Computer Science FAX -- (505) 646-1002 > New Mexico State University http://www.cs.nmsu.edu/~pfeiffer > SWNMRSEF: http://www.nmsu.edu/~scifair
Regards, S. F. Thomas