Re: Information needed

Ralf Mikut (
Fri, 27 Jun 1997 20:47:50 +0200

Dear Mr. Banerjee,

> 1.Can anyone please give me some references on decoupling methods of
> multivariable fuzzy logic control?

Mikut, R.; Bindel, Th; Riedel, E.: Design approaches of fuzzy
controllers for nonlinear multi-level systems and its application to a
coupled pressure-level system. Proc., International Conference Fuzzy
Logic in Enginee-ring and Natural Science (Fuzzy=9296), Zittau, S.
413-422; 1996

Here, fuzzy logic is used to estimate the position in a nonlinear
static characteristic for the actual process situation. On the base of
these results, decoupling factors for a classical approach are
computed using some limitations to improve the security.

A second different approach works with a Petri Net model as a
qualitative model of the system. Using the Petri Net theory, a
reachability graph delivers rules containing also the information for

> 2. I would also like to know, what is the maximum number of rules
> possible for a n x m system, where each input/output has k number of
> membership functions?
> Some papers say it is k to the power n and others say it is k to the
> power of 2m. Which do you think is true. Can anyone please help?

>From my point of view, it should go in the following way:
A system with n inputs and m outputs has k to the power of n
possible "input situations". For these situations, rules can exist
for all m outputs.
If you use m results for each rules - they are k to the power of n
rules. If each rule has only one output fuzzy set the rule base consits of=

m * k^n rules.

Best regards

Ralf Mikut
University of Mining and Technology Freiberg
Institute of Automatic Control
D-09596 Freiberg, Lessingstr.45
phone: ++49-(0)3731-393247
fax: ++49-(0)3731-392925