Re: searching for an overlap measure


Subject: Re: searching for an overlap measure
From: Edward Tunstel (tunstel@helios.jpl.nasa.gov)
Date: Tue May 02 2000 - 17:59:05 MET DST


afaatz wrote:
>
> Hello !
>
> I am searching for an overlap measure (i.e. relative measure of the
> intersection) of two
> fuzzy sets with elements occuring n times (n>=1), i.e. at least once.
> Probably there will be different approaches.
>
> Greetings,
>
> Andreas

Andreas,

You might consider the similarity measure proposed by Dubois and Prade
(Fuzzy Sets and Systems: Theory and Applications, Academic Press,
New York, 1980). If you don't have access to this book, a recent
paper includes some explanation of the formulation and its primary
usage as a measure of the degree of equality between fuzzy sets
(Setnes et al, "Similarity Measures in Fuzzy Rule Base Simplification",
IEEE Trans. Systems, Man, and Cybernetics - Part B, Vol 28, No 3, 1998).

The formulation is:
                          |A intersect B|
                 S(A,B) = ---------------
                            |A union B|
where A and B are fuzzy sets. (The paper also includes an
equivalent expression in terms of membership functions defined
over a discrete universe).

..hope this helps,

Eddie Tunstel

############################################################################
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 : Tue May 02 2000 - 18:13:26 MET DST