An Introduction to Fuzzy Control - Fuzzy Logic: An Introductory Course for Engineering Students - page 174

R1: IF the external temperature is freezing,

THEN the heating demand is large

R2: IF the external temperature is cold,

THEN the heating demand is average

R3: IF the external temperature is medium,

THEN the heating demand is low

It becomes apparent that the meaning of the predicates freezing, cold and medium
is different if the system is intended for Ottawa, Madrid or Dakar, since they would
not be used in exactly the same way. Similarly, the meaning of a large, average or low
heating demand (in a KWscale) is different for a systemmeant to heat an office room,
a conference hall for 200 people or a 25 stores office building. The relative ordering
of the terms large, average and low will certainly be the same, and their shapes will
probably be the same, in all three mentioned cases. Considering one instance of the
problem as illustrated in the figure where it is assumed that the external temperature
is 6 ⓦ C.

fr eezing cold mediu m low av. high

R1

low av. high

R2

R3

-15 6 15

It is fairly obvious that if the external temperature is 6 ⓦ C, the first rule does
not apply, since 6 ⓦ is not considered to be freezing, but “more cold than medium”.
The degree of satisfaction of the premises or conditions stated in the “if” part of
rules 2 and 3 will affect the strength of the corresponding conclusions. This will be
specified by the “then” operation. Rules 2 and 3 are activated to a certain degree and
give proportional suggestions for action. These have to be combined into one single
action by means of an aggregation operation. From the many aggregation operations
that may be used for this purpose, the pointwise maximum is usually the first choice.
The aggregated result is also shown in the figure.
Since it was assumed that finally the water temperature should be proportional to
the heating demand, the fuzzy set representing the aggregation of activated heating
demands has to be converted into a real value through the deffuzzification. This
process will imply an information loss, since it is analogous to representing a signal
with only one coefficient of its Fourier power spectrum. However, experimental
results have shown that “approximating” a fuzzy set by the abscise of its gravity
center or the abscise of its center of area leads to an adequate control performance.