<xoi>

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

>la stivn cusku di'e
>
>> A challenge to all: produce a gismu which can not be considered to be fuzzy.
>
la xorxes cusku di'e
>There are some (e.g. dugri, tenfa, sinso, tanjo) for which it wouldn't be
>very easy to consider them fuzzy.
>
No dice. Fuzzy numbers and fuzzy arithmetic can be easily extended to
logarithms, exponentials, and trigonometric functions by expressing the
Reimann remainder term at the end of the Taylor Series expansion as a fuzzy
interval. There may be a theoretical advantage to expressing the Reimann
remainder in this way. Here's the blurb from the fuzzy FAQ file on fuzzy
numbers:

Fuzzy numbers are fuzzy subsets of the real line. They have a peak or
plateau with membership grade 1, over which the members of the
universe are completely in the set.  The membership function is
increasing towards the peak and decreasing away from it.

Fuzzy numbers are used very widely in fuzzy control applications. A typical
case is the triangular fuzzy number

1.0 +                   +
    |                  / \
    |                 /   \
0.5 +                /     \
    |               /       \
    |              /         \
0.0 +-------------+-----+-----+--------------
                  |     |     |
                 5.0   7.0   9.0

which is one form of the fuzzy number 7. Slope and trapezoidal functions
are also used, as are exponential curves similar to Gaussian probability
densities.

For more information, see:

   Dubois, Didier, and Prade, Henri, "Fuzzy Numbers: An Overview", in
   Analysis of Fuzzy Information 1:3-39, CRC Press, Boca Raton, 1987.

   Dubois, Didier, and Prade, Henri, "Mean Value of a Fuzzy Number",
   Fuzzy Sets and Systems 24(3):279-300, 1987.

   Kaufmann, A., and Gupta, M.M., "Introduction to Fuzzy Arithmetic",
   Reinhold, New York, 1985.

la stivn cusku di'e
>> le rozgu pafi'uci xoi barda le ka melbi kei le mi'o ckilu
>>
>> The rose is fuzzily 1/3 big in property beauty on our (predefined) scale.
>
la xorxes cusku di'e
>Rather:
>
>The rose is big in property beauty compared to our scale.
>(truth value of that sentence = 1/3)
>

If this is how you are translating <xoi>, how is it different from <jei>?
You are not using <xoi> in the way and originally proposed. Here's what and
wrote:

la 'and cusku di'e
>If a lujvo, something including {murse} "dawn/dusk" might be good.
>But this isn't the job for a brivla, for if you are content with
>a brivla then we already have what you need: {jei}.

>   li pi mu jei mi clani
>   "O.5 is the truth value of that I am tall"
>
>In contrast, I want us to be able to say
>
>   mi pi mu xoi clani
>   pi mu xoi ku mi clani

As I've mentioned earlier, I am still baffled as to why you and and are
using <clani> to mean "long" in contrast to "short" instead of "has length"
which is what the dictionary says <clani> means. Where did this use come
from, and where is it documented?

la xorxes cusku di'e
>The x3 of {barda} is not for a scale, but for something with which to
>compare the x1. You would be saying that the rose is big in beauty compared
>with how big our scale is in beauty.

True, I should have used mi'a.

le rozgu pafi'uci xoi melbi ma'i le mi'o listyckilu

"The rose is fuzzily 1/3 beautiful on our ordinal scale."
or
"The rose is beautiful to fuzzy extent 1/3 by the standard specified in our
(previously agreed upon) ordinal scale."

I would also like to have fuzzy scales which apply to an interval between
two "pure" colors:

letu ka rozgu kei cu skari refi'umu xoi xunrypelxu ma'i le mi'o listyckilu

"The color of yonder rose is fuzzily 2/5 red-yellow on our ordinal scale.
or
"On our ordinal scale which ranges from pure red to pure yellow, yonder
rose has the color fuzzy 2/5 red-yellow."


co'omi'o la 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