fuzzy questions

["Steven M. Belknap" <sbelknap@UIC.EDU>]

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