Explicit fuzziness (was: Re: ConNumbers)

> Interesting!  I know that fuzzy systems mathematicians have worked out
> perfectly usable systems of "fuzzy numbers," where "fuzzy one," "fuzzy
> two," and "fuzzy three" and so on are actually graded categories with
> peaks at the points we would call one, two, and three respectively,
> and decreasing degree-of-membership curves as you move away from that.
>  (For example, what we call the number "two" could be expressed in
> such a system as either "fuzzy two to degree 100%" or "fuzzy one to
> degree 20%" (or some similarly low number) or "fuzzy one hundred to
> degree damn close to zero".
>=20
> Of course, then you need standard numbers to mark the degree of
> categorial membership, but you can fuzzify *those* numbers, and so on
> recursively, so you *never* get nailed down to anything!
>=20
> We have such numbers in our own natlang vocabulary, of course, but
> they're derivative: "about four" or "four-ish" can be expressed as a
> fuzzy set which has a membership curve that peaks to 100% at four, and
> trails off in either direction.  The speed with which it trails off
> would depend on context, of course.
>=20
> So, yeah, such a system is conceivable, and kind of cool!
One already exists.. and not just for numbers.  Danoven/Aroven includes
a measurement, a "strength" and an uncertainty system for all conceptual
links -- the measurement system may but does not necessarily entail actual
quantification, e.g. "the building is *very* high", or "the building is
so-many-stories high".  The uncertainty factor has to do more with actual
quantification, e.g. "the building is 100 stories high, give or take 10
stories", "the glass was *about* half full".  The strength has to do with
the certainty of both of the preceding descriptions, e.g. "the building
is very high, and I *know* that", or "the building is around 100 stories
high, or so I'm given to believe".  So, if you're going to be uncertain
in Aroven, at least you can be *definitely* uncertain :-)

Josh

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