(A) often smaller than the crisp partitions inherent in a crisp rule, eg.
with T crisp:
IF (T > T_min1) AND (T < T_max1) THEN (Current = 2.5 V): an action valid
for the nonoverlapped interval [T_min1,T_max1];
(B) The FLV is almost always overlappartitioned into fuzzy termsets.
of an intuitive *linguistic* nature such as {..., ME[dium],HI[gh]}.
Also missing in crisp rulebases is the "Linguistic Hedge" or the
possibility to modify these terms eg. Very HI = HI^2, or mu_HI(T)^2, again
highly intuitive.
(C) Then the fuzzy inference engine (FIE) processes all the inputs using
fuzzy logical operations which *appear* similar to the crisp IE, but have
a more compact [fuzzy] rulebase (FRB). Modifications to the FRB are easy
to do, and simple to understand, far oftener than the Crisp RB (CRB).
(D) Then it has been shown that a fuzzy model structure has the property
of a Universal Approximator (UA) : given a smooth function F(T), one can
always construct a fuzzy model F_fuz(T) ~~ F(T), for all T in
[T_min,T_max]. This property does not exist for a CRB model.
There exist good GUI's that directly generate a Fuzzy Model [in C++ say]
to test in a real/simulated case.
In Fuzzy Logic Control (FLC), which is my area of interest here, one does
not actually look at the FRB of an FLC to compare with a crisp expert
system. The "expert system" role, in fact the "logic" part of the fuzzy is
suppressed in FLC  which is treated as an input/output *controller*
block typically replacing a [linear] PID controller. The UA property makes
the FLC a *nonlinear* controller, in general.
Pramit
On Thu, 17 Jun 1999, Peter Hirsch wrote:
> I understand that fuzzy logic allows the implementation of rules to control
> a situation. (I refer to Fuzzy Tech's application note about a boiler
> temperature control system for a home heating system in which 405 rules were
> identified. (www.fuzzytech.com/e_a_esa.htm) I also have read that this sort
> of rule based logic is difficult to implement with conventional logic and
> code. Could somebody explain this a little bit more? I don't understand
> where the difficulty lies.
>
>
>
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============================================================================
Pramit "Jake" Sarma
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email: jake_n_jazz@yahoo.com email: psarma@che.iitb.ernet.in
Process Systems and Control
The PROCISS Group

{Mathematics/Physics}<Applied NonLinear Control>{Industrial World}

Process Control, Identification & Simulation Systems
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