An interesting thing about fuzzy rule-bases (FRB's) which is not
sufficiently mentioned (in the open literature, at any rate), is that
certain fixed FRB's do pretty well for a rather broad, often not
obviously related, set of commonly nonlinear processes. For example,
assume a (2n-1)-level equal grid, around some fuzzy centre, for a 2 x 1
(TISO) FRB, typical of FLC's. N = 2n-1 is the net grid, though this form
tends to imply near-symmetry [of fuzzy term geometry, or the FL Var
(FLV))]. For ease of argument, also assume equigrids, or NA = NB = N
(easy to extend to non-square odd NA, NB). It's a decent starting point,
and for compactness let's call it a N-FRB:
A very useful basis/skeleton FRB is the what can be called the 'cross',
with rules only along the 'spine' (A = ZO or B = ZO), and has a nice
algebraic relation for number of rules M = 2N+1 = 4n-1. All other rules
are set to 'inaction' or 'do-nothing'. The origin of this N-FRB is misty
(to me), though I recall Mamdani possibly being the source (any
comments?). If it's workable, then it also has the advantage of *not*
having combinatorial problems, as it is a linear fn(N). This is used in
a set of special nonlinear plants, including the famous inverted
pendulum (eg. Kosko, 1992), with at most a 'perturbation'-addition (of 2
'extra' rules). Other similar N-FRB's can be seen in the Matlab Fuzzy
Logic Toolbox of Jang and Gulley (1995 onwards). Clearly the rule-count
<= N^2 = M_{max}.
In part of my current work, the unmodified 'cross', or (2n-1)-FRB of
exactly 4n-1 rules worked in one fairly nonlinear reactor model: and
what was interesting is that it worked equally well for (a) a simple
level-control loop, and (b) a highly nonlinear temperature-control (I
used n=4 == N=7). [It also outperformed every 'hard' controller]. For
anyone investigating self-organising FRB's, it would seem to be the next
best starting guess over a blank FRB, possibly. So, this simple little
FRB has already more than one use: level, temperature, and joint-angle
control. All other FRB's can even be considered, qualitatively, as
"augmentations" of this base, possibly. One such general base FRB is
provided by Yamazaki and Sugeno (1985), and a quick reference to spot it
it is in the book "Fuzzy-Neural Control" by Nie and Linkens (1995). It
has n=4 == N=7 fuzzy gridding, and is a 33-FRB, where M_{max} = 49. It
was evolved heuristically from a composite of processes (more details in
the 1985 paper).
It is plain to see that a N^2-FRB can always be constructed. However,
the advantage of each blank-rule is that is ignored for the calculations
of fuzzy output - and an FIE fires all rules and composites them.
Therefore, there is a penalty for higher M: more computational load, and
this is one motivation behind trying to choose M < M_{max}. It is very
system-specific, especially for speed. For high-speed calculations, it
may be critical (hence fuzzy chips); for others, not so much. The other
penalty is of course, the very combinatorials or the difficulty of
identifying M_{max} rules.
Clearly it is a sub-topic that warrants considerable further research;
and such an FRB-library also should be open to all fuzzy systems
researchers for access. Good books for searches are "Industrial
Applications of Fuzzy Logic", Ed. M. Sugeno, 1985; "Neural Networks and
Fuzzy Logic", B. Kosko, 1992; "Fuzzy Systems Theory and Applications",
T. Asai, M. Sugeno and T. Toshiro, 1992.
Subject:
RFI - Rule sets - pre-built - domain-specific foundation rules -
availability or
contacts
Date:
Wed, 24 Nov 1999 19:39:57 +0100 (MET)
From:
Eric Marceau <marceau@nortelnetworks.com>
To:
Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
I am looking for pre-built libraries of rule sets appropriate to
specific technical domains. My view is that availability of
such ready-to-use rule sets would:
- accelerate the use of the technology
- standardize the approach to knowledge classification and attributes
- facilitate the overall discussion of management of knowledge
characterization such as hypothesis, scenario, proposal, confirmed,
dated, obsolete and the life-cycle management of knowledge base items.
- reduce the effort to advance beyond the technology assimilation into
the technology application phase
My particular interests are manifold, but specifically relate to two
career interests:
- computing system status and performance monitoring (currently in
Design-to-Manufacturing IS)
- manufacturing engineering process planning (past carreer and hopefully
future return)
I would appreciate any hints as to sources/contacts for such rule sets
which are either
- available now
- under development and seeking end-user reality check
Thank you,
Eric Marceau
marceau@nortelnetworks.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
--
"Vasudhaiv kutumbhakam" - The World is one family
==========================================================================
Pramit 'Jake' Sarma
[Home] [Lab]
e-mail: pramits@Vsnl.com psarma@ChE.IITB.ERnet.In fax : (91-22)-578-3480 s-mail: (on request)
Process Systems and Control The PROCISS Group | {Mathematics/Physics}-<Applied NonLinear Control>-{Industrial World} | Process Control, Identification & Simulation Systems ==========================================================================
############################################################################ 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