In one fuzzy sets theory textbook, I found the following description.
"... They define a membership function in a similar way to the
possibilistic method of inducing a possibility function from a histogram:
Ms(x) = kp(x) if kp(x)<1, and
= 1 if kp(x)>=1.
where p(x) is the probability density function for x on S and k is a
constant to be solved for by solving
kF(p(x))-c = 0,
where F(p(x)) is the integral of (p(x))^2 dx over the region for which
kp(x)<1 plus the integral of p(x)dx over the region where kp(x)>=1, and c
is the desired confidence level."
My question is how to obtain the F(p(x)) and why it has relation to
confidence level c? I have no cue.
Thanks a lot!
############################################################################
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