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*To*: John Cowan <cowan@LOCKE.CCIL.ORG>*Subject*: fuzzy questions*From*: "Steven M. Belknap" <sbelknap@UIC.EDU>*Date*: Sun, 26 Nov 1995 15:52:23 -0600*Reply-To*: "Steven M. Belknap" <sbelknap@UIC.EDU>*Sender*: Lojban list <LOJBAN@CUVMB.BITNET>

and proposed a new selmao, <xoi> for fuzzy things. This would be great! But, I have two questions. 1. In my previous post, I wondered if a single selmao was enough to get the job done, and suggested that 4 new selmao in this new family <XOI> were needed, one for each of the scales (nominal, ordinal, interval, ratio). Is there another way to specify scale and use xoi for all fuzziness? Note that any measurement which can be expressed in a given scale can also be expressed in all lower scales: ratio: Wilt Chamberlain is 6% taller than Bill Russell. interval: Wilt Chamberlain is 4 centimeters taller than Bill Russell. ordinal: Wilt Chamberlain is taller than Bill Russell. nominal: Wilt Chamberlain is tall. 2. How do we express confidence intervals? The problem of confidence limits is evident when and's examples are changed to interrogatives. mi pi mu xoi clani "I am fuzzily tallish to extent 0.5." (Ratio scale implied) pi mu xoi ku mi clani "fuzzy extent 0.5 is a quality/property of my height." Those are o.k. They are elegant, compact expressions of fuzziness. But the problem of scale specification raises its ugly head when these are expressed as interrogatives: xu do pi mu xoi clani What does this mean? Does it asking if I have *exactly* 0.5 tallishness? Then we have lost the fuzzy. Suppose I consider myself 0.6 tallish. Should I answer <go'i> or <na go'i> to this question? Is the question unanswerable? Is there a good fuzzy answer? The <go'i> vs. <na go'i> dilemma is raised by the non-fuzziness of these cmavo.In order to answer rationally, I need to know what type of scale is being used. The 0.5 suggests it is not a nominal scale. It must not be ordinal or interval either, or I would know from the question what the implied granularity is. So its a ratio scale. But what degree of second order fuzziness would permit a <go'i>? If this is a ratio scale, I need to answer this question in a hedging fashion with explicit specification of confidence intervals, thus preserving fuzziness, but maintaining Aristotlean dichotomy. mi pi mu xoi <confidence interval + or - 0.1> clani Before you all think this is hopelessly artificial, here is a conversation I had recently in English: Person 1: So what are you, about 6'1"? Person 2: Yeah, within a couple of inches or so. In the context of the conversation, giving my exact height (5'11 1/2") would have been mildly inappropriately precise. If you listen to people, you'll hear this sort of thing a lot. (Particularly if you have friends who are lawyers!) Here's another I've heard: Person 1: So the train gets in at 2? Person 2: Plus or minus 10 minutes. If you listen, you'll hear fuzzy confidence intervals fairly often. the <xao> selmao raises some of the same issues as discussed in the negation paper, which I guess is not surprising for things which are somewhat true and somewhat false. Ideas? co'o mi'e. stivn. Steven M. Belknap, M.D. Assistant Professor of Clinical Pharmacology and Medicine University of Illinois College of Medicine at Peoria email: sbelknap@uic.edu Voice: 309/671-3403 Fax: 309/671-8413

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