Message-Id: <199602281908.OAA05396@locke.ccil.org>
Date:         Wed, 28 Feb 1996 11:59:48 -0600
Reply-To: "Steven M. Belknap" <sbelknap@UIC.EDU>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: "Steven M. Belknap" <sbelknap@UIC.EDU>
Subject:      kamkuspe
To: John Cowan <cowan@LOCKE.CCIL.ORG>
Content-Length: 3406

I keep meaning to ask more about <fiuhi>, which John Cowan proposed several
weeks ago, and which I (unintentionally) neglected to give as a possible
substitute for <xoi> in my last fuzzy post. It sounded interesting, as it
would do some fuzzy things I would like to do, but I wasn't so sure about
the X3 place. (I didn't mean to neglect <fiuhi> in my previous fuzzy post,
I am just exploring different aspects of fuzzyness which may already exist
in lojban, as suggested by lojbab.) <fiuhi> seems like a valuable addition.

john:
> 2) for scalar claims generally, a new cmavo of selma'o MOI (for
> discussion purposes, "fiu'i"), with tentative place structure:
>        x1 is at <number> location on scale x2 (of type x3?)
> I'm not sure if x3 is useful; it is meant to be filled with things like
> "cardinal", "interval", etc.
> Comments?

Would these be correct usage?

<levi rozgu 2/5 fiuhi melbi kei lo kamklesi>

"This-here rose is a fuzzy 2 out of 5 on a categorical/nominal beauty scale."

Since such a nominal scale would be unordered, there is no implication that
a 3/5 score is any better than a 2/5 score, but there is a fuzzy boundary
between the 6 groups, which are denoted by the labels
(0/5,1/5,2/5,3/5,4/5,5/5). For example, perhaps six people brought roses to
the show, and Joannes roses are designated as 0/5, while Brenda's roses are
designated by 1/5, but some roses were partially cultivated by Brenda and
partially by Joanne, so the classification is fuzzy, rather than discrete.


<levi rozgu 2/5 fiuhi melbi kei lo kamporse>

"This-here rose is a fuzzy 2 out of 5 on an ordinal beauty scale"

An ordinal scale is ordered, but the distance between membership apices are
possibly unequal. Thus a 4/5 rose has a higher beauty score than a 3/5
rose, but the distance along the scale from the membership apices 2/5 to
3/5 is not necessarily the same as from 3/5 to 4/5.


<levi rozgu 2/5 fiuhi melbi kei lo kamgradu>

"This-here rose is a fuzzy 2 out of 5 on an interval beauty scale."

An interval scale requires equal spacing among the apices of the fuzzy
sets, so interval arithmetic using addition and subtraction with the apices
(or fuzzy arithmetic with the actual sets) will work, although the 0/5 is
possibly arbitrary, and so multiplication and division are not valid.


<levi rozgu 2/5 fiuhi melbi kei lo kamparbi>

"This-here rose is a fuzzy 2 out of 5 on a ratio beauty scale."

Same as interval, but now the zero is a true zero, so multiplication and
division work.


I do not see how <fiuhi> can describe fuzziness in the semantic space
between two constructs;my previous example was paint which was a blend of
red and yellow. 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?

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. Comments on my
above translations of (nominal, ordinal, interval, ratio) as applied to
scale would be appreciated.

Also, I am still wondering about nika for fuzzy property abstraction.


cohomihe la 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