Re: fuzzy sets--rough sets?


Subject: Re: fuzzy sets--rough sets?
From: Will Dwinnell (predictor@compuserve.com)
Date: Wed Mar 01 2000 - 12:37:20 MET


Zunt wrote:
"I noticed someone make a distinction between fuzzy and rough the other day, but he
didn't
elaborate and it's not one with which I'm familiar. I know about fuzzy sets--can
someone please give me a clue about rough sets?"

The basic idea behind rough sets is that while some cases may (using the input
variables) be clearly labeled ("predicted") as being in a set X (the "positive
region"), and some cases may be clearly labeled as not being in set X (the
"negative region"), limited information prevents us from labeling all possible
cases clearly. The remaining cases, which cannot be distinguished based on the
input variables lie in what is known as the "boundary region". Rough sets theory
calls the positive region a "lower approximation" of set X, which yields no false
positives. The positive region plus the boundary region make up an "upper
approximation" of set X, which yields no false nagatives. The practical end of
rough sets theory deals with binning continuous inputs and deciding which areas of
the input space should be included in these various approximations.

I'd suggest checking some of the rough sets Web sites- they have diagrams which
make all this more plain.

Will Dwinnell
predictor@compuserve.com

############################################################################
This message was posted through the fuzzy mailing list.
(1) To subscribe to this mailing list, send a message body of
"SUB FUZZY-MAIL myFirstName mySurname" to listproc@dbai.tuwien.ac.at
(2) To unsubscribe from this mailing list, send a message body of
"UNSUB FUZZY-MAIL" or "UNSUB FUZZY-MAIL yoursubscription@email.address.com"
to listproc@dbai.tuwien.ac.at
(3) To reach the human who maintains the list, send mail to
fuzzy-owner@dbai.tuwien.ac.at
(4) WWW access and other information on Fuzzy Sets and Logic see
http://www.dbai.tuwien.ac.at/ftp/mlowner/fuzzy-mail.info
(5) WWW archive: http://www.dbai.tuwien.ac.at/marchives/fuzzy-mail/index.html



This archive was generated by hypermail 2b25 : Thu Apr 06 2000 - 15:59:46 MET DST