transitive closure

formato ferrante (formato@bridge.diima.unisa.it)
Mon, 16 Nov 1998 04:04:56 +0100 (MET)

Hello everybody
Given a continuous t-norm * and fuzzy relation R on S, what is the
*-transitive closure t(R) of R?
I made some computations and I found
t(R)=sup_{i in N} R^i

where R^i is the usual power of R obtained by composition.
Is my result correct?
Valverde, in his paper on F-indistinguishability ops, quoted
an old result of Kaufmann, adding that R shall be reflexive, but
I dod not use this hypothesis in the proof.
thank you
ferrante formato

############################################################################
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