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Date:         Wed, 28 Feb 1996 23:15:35 -0600
Reply-To: "Steven M. Belknap" <sbelknap@UIC.EDU>
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From: "Steven M. Belknap" <sbelknap@UIC.EDU>
Subject:      Tech: fuzzy: kamkuspe
To: John Cowan <cowan@LOCKE.CCIL.ORG>
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>la stivn cusku di'e
>
>>  Is there some slick way that I can say:
>>
>>"The paint is fuzzily 2 of 5, where 0/5 is red and 5/5 is yellow."
>>
>>Ideas?
>
la xorxes cusku dihe
>How about:
>
>  le cinta cu klani li ji'irefi'umu le kamxunre bi'o le kampelxu
>  The paint is approximately 2/5 on the ordered interval from red to yellow.
>

That looks interesting. I like the use of biho, although it might be
problematic for a categorical Guttman scale. <jihi> is not an accurate
translation of the technical sense of "fuzzy", which is the sense I meant.
Your translation of  <jihi> as "approximately" seems right. Is it OK to use
cinta or do you need to explicitly say the paint color when you translate
into lojban? Do you need to abstract the colors, which are already
abstractions? How about:

<le cinta selskari ko refi'umu fiuhi le xunre bi'o le pelxu>

"The color of the paint is fuzzily 2 of 5 on the ordered interval from red
to yellow."

This seems intuitively reasonable. It also would require no additional
cmavo-a big advantage as we approach the time when the refgrammer will be
chiseled into granite. I think application to intervals in semantic space
can be justified as a reasonable overload to the <fiuhi> cmavo.

Consider:

<le cinta selskari ko refi'umu fiuhi le pelxu>

"The paint-color is fuzzily yellow to extent 2/5."

If we consider <fiuhi> to be an operator which specifies the extent of the
color on the ordered interval from absent yellowishness to complete
yellowishness, then the application of <fiuhi> to <le xunre bi'o le pelxu>
seems reasonable. From this perspective,

<le cinta selskari ko refi'umu fiuhi le pelxu>

is logically equivalent to:

<le cinta selskari ko refi'umu fiuhi le na pelxu bi'o le pelxu>

This approach could obviously also be used to express a scale with a polar
negation end-point. To explicitly specify an ordered scale from the
opposite of yellow (say blue on the color wheel) to yellow, one could use:

<le cinta selskari ko refi'umu fiuhi le tohe pelxu bi'o le pelxu>

>>I am wondering about the fraction or slash cmavo. Is there an official
>>position on whether this cmavo means division? Or can it mean 2 of 5 as I
>>used above? & and lojbab seemed to disagree on this point.
>
>I don't see the difference. I would understand it in the same way if you
>say that the paint is 0.4 on the interval that goes from red to yellow.

They have different granularities. In a <fiuhi> fuzzy statement, the
speaker specifies both the granularity (number of fuzzy sets) and the
specific set. Thus

<le cinta selskari ko 2/5 fiuhi le xunre>

and

<le cinta selskari ko 4/10 fiuhi le xunre>

have different meanings. In the first statement, the speaker is specifying
that six fuzzy sets are used and in the second statement the speaker is
specifying that eleven fuzzy sets are being used. The process of taking a
continuously variable property and turning it into a fuzzy set designation
is called "defuzzification." This doesn't mean that we have gone to
discrete sets, it just means we have chosen the best of several fuzzy sets
to represent our fuzzy assessment of the position of the variable. The
names of the sets (0/5,1/5,2/5,3/5,4/5,5/5, respectively), are discrete, of
course, but they represent fuzzy sets.

The discreteness of most English utterances may not obtain in other
languages. For example, the use of tones in some Asian languages has been
claimed as an example of linguistic fuzzy sets, but I don't know of any
examples of this. All the tone-meanings I've heard about completely change
the meaning of the word. There may be some examples of fuzziness in jazz
music too. I await authoritative analysis from fuzzy linguists on these
points.

cohomihe kamkuspe 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