Hi Chris,
A Boolean variable is bivalent – it can
take on True or False as its value. A multi-valent variable can be True
False or Unknown, as you define it. Rough sets are multivalent because
their boundaries are not crisply defined. They can be in the set, out of
the set, or in the bracketing upper and lower boundaries.
The meaning of the upper and lower
boundaries depends on how the boundaries are defined. They can be used to
model and process uncertainties of various kinds.
There is a long history of multivalent
architectures, tagged architectures, and various other ways investigated for
finding a set in a discovery process. Most of it was in EE areas, where
sensors can provide mixed logic and scalar measures. Especially in
electronic warfare, multivalent variables are often used to delay making the
True or False decision until more information is available about the boundary
sets.
HTH,
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
Sent: Friday, January 14, 2011
6:01 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum]
Ontology of Rough Sets
On Jan 14, 2011, at 4:16 PM, Rich Cooper wrote:
Azamat,
Agreed, rough set theory is a different
view of sets, not probabilistic, not fuzzy,
Rough sets differ formally from fuzzy
sets in some important ways, but they are certainly kissin' cousins. Both
were designed to deal with vagueness and imperfect knowledge, and the idea of
the boundary region of a rough set is meant to do the same sort of work that
fuzzy membership was designed to do. Indeed, it is possible alternatively to
define rough sets in terms of a rough membership function, which turns out to
be a generalization of fuzzy membership.
not ambiguous, but bounded and
multivalent.
Rough sets have boundary regions; I
don't know what you mean by saying they are bounded. And I have no idea what
you have in mind in calling them multivalent.
|