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*To*: John Cowan <cowan@LOCKE.CCIL.ORG>*Subject*: Re: various fuzzy matters*From*: Jorge Llambias <jorge@PHYAST.PITT.EDU>*Date*: Tue, 28 Nov 1995 18:35:01 -0500*Reply-To*: Jorge Llambias <jorge@PHYAST.PITT.EDU>*Sender*: Lojban list <LOJBAN@CUVMB.BITNET>

la stivn cusku di'e > Actually, I'm not sure what > > la djan clani > > means. (I was so interested in fuzziness, that I confess I did not look up > the definition of <clani> when and gave it as an example.) It means: "John is long (in longest dimension, by some standard)." > Would this translate as "John has height."? Not really. A better way to say that would be: la djan ckaji le ka ke'a sraji mitre John has the property of being something in vertical meters. John "having height" does not imply that he is tall. Even the shortest person has height. > la djan cu barda le clani > > seems closer to "John is tall." in the sense of an unspecified external > standard. {le clani} means "the long one(s)", so {la djan cu barda le clani} means "John is big in the long dimension" which seems fine. > How about > > la djan barda le clani mi > > "John is tall compared to me." That seems ok. In the case of {barda} the wording of the definition suggests that the x3 is what you compare with the x1. > To get fuzzy, I would use an interval scale; if the proposed selma'o <xoi> > is to be used: > > la djan pi mu xoi barda le clani le cnano > > "John is to fuzzy extent 0.5 taller than normal." [...] > Note how numbers are being used here. There is not a 1:1 correspondence > between height and the fuzzy tallness <xoi bardi le clani> of the person! > (There seems to be a pervasive misunderstanding of this point.) I'm afraid that the pervasive misunderstanding persists. You tell me that "John is to fuzzy extent 0.5 taller than normal". I then tell you that "Mike is to fuzzy extent 0.6 taller than normal". Are we allowed to conclude that Mike is taller than John? If yes, how did we manage to get to this if you don't know Mike and I don't know John, and we never discussed their actual heights? If no, then what are we using the numbers for? It is not even an ordinal scale, because it doesn't allow us to compare their heights. > If we were > explicitly specifying a fuzzy tallness function, it might be something > like: > > 0 for all persons shorter than 160 cm > 1 for all persons taller than 200 cm > > linearly increasing from 0 to 1 for all persons between 160-200 cm in height. Ok, let me get out my calculator, Mike is 1.75m, so in fuzzy he comes out to be (175-160)/40 = 0.37. I was wrong, I should have said "Mike is to fuzzy extent 0.37 taller than normal", and now we can conclude that he is shorter than John, who is 0.5 fuzzy tall (or 1.80m). Obviously, to use this specific scale we need a calculator handy, so we won't be using it in general. But if we don't have a specific scale, the numbers that you come up with cannot be meaningfully compared with those that I come up with, so when is it appropriate to use them? > Thus, this is an interval scale, not a ratio scale, as we are using > arbitrary cutoffs for fuzzy tallness. But where did the specific choices of > 160 and 200 cm come from? From a prior implicit or explicit understanding > between speaker and listener, of course! I might imagine the following > conversation: > > Person 1: I want to talk about human tallness. > > Person 2: O.K. What fuzzy norm should we use? > > Person 1: I think that anyone shorter than 160 cm is definitely not tall, > and that anyone taller than 190 cm is definitely tall. > > Person 2: Actually, I would choose 200 as the top cutoff. > > Person 1: O.K. And I want to use a linear function for instances of tall in > the interval 160-200 cm. > > Person 2: O.K., I accept that. So we agree on a fuzzy norm. > > Person 1: la djan papino xoi barda le clani le cnano > > Person 2: go'i Can you really imagine that conversation taking place in real life? And what about people who can't do all the necessary math in their head? Isn't it much easier for us just to talk about the actual heights? > Of course, speaker and listener might choose to leave the exact fuzzy norm > unspecified, or might use a different function; If they leave it unspecified, how can they understand each other? "John is 0.43 fuzzy tall", "No he's not, he's obviously a 0.56", "What do you mean 0.56, can't you tell he's a 0.43?" etc. > in this case, any > monotonically increasing function mapping [0,1]:>[0,1] will do. I guess you mean [0,large enough):>[0,1] > I am unsure > how to elegantly describe the fuzzy function explicitly in lojban. You could probably describe it as elegantly as in English, but when would you want to use it? If you know the actual height, you can use the actual height with much less trouble. If you don't know the actual height, then the function is pretty useless. (I'm not saying that it is useless as a model to store subjective data, I'm saying that it is not very meaningful in direct speech.) Jorge

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