Fuzzy Inference
A room's light density serves as the input and
it
is a crisp, measurable (physical) value. To perform fuzzy
inference, the fuzzy system converts this physical value into a fuzzy
(discrete) value. The fuzzy inference uses this value along with the
fuzzy knowledge base to determine a resultant value that the fuzzy
system then converts back to a physical value. This process consists
of:

· Fuzzification 

· Fuzzy Inference 

· Defuzzification 
and is expanded below.
Fuzzification
The fuzzy system checks the physical input value
for memberships in the fuzzy linguistic sets and the
membership value is calculated. Define m(u) as the membership value
of the input and u as the value of the natural light. We use the following
simple sets of formulas to define this:
m(u) =

0 for u < a 

(ua) / (ba) for a <= u <= b 

(cu) / (cb) for b<= u <= c 

0 for u > c 
(Yan, Ryan and Power, 1994)
Where a, b and c are the values of the fuzzy sets
as described in Figure 1 and u is the input crisp value.
For the fuzzy set Low_Light the values would be a = 5, b= 10
and c=15.
If the input value (light density) is less than
'a', then
m(u) would be zero; If it is greater than or equal
to 'a' and less than or equal to 'b' then m(u) is calculated by the
formula
(ua)/(ba).
Since u and a, b, c are known, the membership
value m(u), can be calculated. A crisp input value
may fall into several fuzzy linguistic sets if the light density meets
the membership conditions for both the low and high light set. The
membership function for each fuzzy linguistic set is calculated, using
the above sets of formulas, before the fuzzy inference (See Fig 2).
The following illustrates the output of this step:

The input crisp value u:
Belongs to the fuzzy linguistic set 


LOW_LIGHT to degree of x
i.e. m low_light (u) = x 

Belongs to the fuzzy linguistic
set 


HIGH_LGHT to degree
of y
i.e. m high_light (u) = y 
Fuzzy Inference  Expanded
We now know which fuzzy sets the input value
belongs to and the fuzzy values corresponding to our


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input crisp value. Using the above output and the fuzzy
knowledge base, the output electric voltage must be low to the degree
of y and high to the degree of x, or:

IF light = "high" 


[m high_light (u) = y ] 

THEN electric_voltage = "low"

Therefore, the output electric voltage must be low
to the degree of y:

IF light = "low" 


[m low_light (u) = x ] 

THEN electric_voltage = "high" 
Therefore, the output electric voltage must be high
to the degree of x.
How is the output low and high at the same time?
The typical power supply unit does not 