On combinatorial explosions

Bob Dalton (red@swl.msd.ray.com)
Sat, 6 Jun 1998 19:58:52 +0200 (MET DST)

Ranier Holve writes that there is a combinatorial explosion with n
inputs and m fuzzy sets => m^n rules:

>> Actually, the number of possible rules grows exponentially with the
>> number of inputs, i.e. n inputs with m fuzzy sets -> m^n rules.

Coombs and Andrews, IEEE Trans. Fuzzy Sys 6:1, pp 1-11, 1998 say
otherwise, i. e. that the "curse of dimensionality" is no more. I believe
this was ther reference Siler was referring to.

Reading the Coombs paper, I can see how the exponentiality is addressed,
but what I don't see is how the fidelity of the implications of the
original (exponential) rulebase is retained: i. e. how the mn "new"
rules imply the same thing the m^n "old" rules implied.

Neither Coombs or Holve provides a reference for [Bellman] and the
binary tree representation. It might be important.

--------------------------------------------------------------------
--------------------------------------------------------------------

Robert E. Dalton, Ph. D. email: red@swl.msd.ray.com

Raytheon Co. Mailstop: T3MN35 voice: (978) 858-5927

50 Apple Hill Drive, Tewksbury, MA 01876

--------------------------------------------------------------------
--------------------------------------------------------------------

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