In article <3B674E1D.F47314AF@verizon.net>, S. F. Thomas writes:> Stephan Lehmke wrote: >> >> My standard counterexample is an orange. >> >> While nobody in their right mind would say that an orange is `red', I >> bet a lot of people would agree it's at least `somewhat red'. So while >> the probability that an orange would be called `red' might be zero, >> I'd give it a non-zero membership degree in the in the fuzzy set of >> red objects. > > I don't see how this is a counter-example. This IMO simply confounds > two different terms, namely "red" and "somewhat red", and implies a > usage which is incorrect in my opinion, namely that for something to > be describable as "somewhat red" is to concede that it is perforce > also "red". I don't think that is necessarily true. It is the same > as > saying that if someone is "not tall" that they are perforce "short". > The implication should rather go the other way; the narrower term > implies the broader, not the other way around. It would be like a > witness testifying in courst that the orange she had for breakfast > was > "somewhat red", or a "reddish orange", only to have a too-clever > lawyer > seek to impeach the credibility or mental competence of the witness > by insinuating that she claimed to eat "red" oranges! > Be that as it may, I don't see that there is any difficulty posed > in principle for a polling procedure that takes an exemplar of > *any* shade of "reddish orange" or of "orange red", or indeed of any > shade of color whatsoever, and obtains its corresponding > characteristic > (membership) value in the manner described, for any term of color, > "red", "reddish", "somewhat red", "orange red", or whatever.
Just two remarks: * To me, fuzziness is all about comparability. I don't really care what the exact membership degrees are, as long as I can successfully use them to rate whether one object corresponds better or worse to a fuzzy concept than another. So, if it is sensible to say that an orange is `strictly more red' than a lemon, then the membership degree of the orange in the fuzzy set of red objects can't be zero. * 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.>> 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.
Rating vague concepts on scales is very common everyday practice. To give people more familiarity, one could use a scale of grades like those used in school, which make perfect membership degrees for fuzzy sets. regards Stephan