Fuzzy Logic
Since its discovery by Lotfi Zadeh in 1965, practical
applications of fuzzy logic are on the rise. Envisioned
as one of the world’s ten hottest technologies starting the twentyfirst
century (Ross, 1995), it has lived up to these expectations, based
on the number of fielded applications.
Fuzzy logic’s success is due, in part, to its resemblance
to
human thinking and decisionmaking. Humans do not view
the world as stark binary values — black or white, yes or no; but
rather in varying degrees of correctness. We understand tall,
yet tall has no finite defined value. We are quite comfortable with
a set of values that we considered as tall. Furthermore, we
cannot satisfy all real world problems with a binary twostate logic
– most problems are not solved with a yes/no answer. Since a key goal
of AI is modeling human intelligence and the manner in which humans
think, fuzzy logic supplies a mechanism for modeling this crucial
aspect of human thinking.
To illustrate key fuzzy logic fundamentals, this
article defines a simple methodology that is applicable
to real world problems as well as illustrates an implementation model
built in PDC’s Visual Prolog. (A free personal edition of Visual Prolog
is available for download from www.pdc.dk).The
example application is a ‘fuzzy energy saving bulb and controller’;
based on a normalized, T shaped, symmetrical membership function
output or in layman’s terms, a simple bell shaped distribution curve.
Since the output typically must be discrete values, defuzzification
is required to convert the fuzzy result into exact output values.
This implementation uses the Weighted Average Method to perform this
defuzzification. Briefly, a Weighted Average Method starts with a
sequence of function values and a matching sequence of real numbers,
called weights, where the sum of all of the weights is one. The sum
of all products of the weights times the function values is defined
as the function values weighted average. 

The Case of the Electric
Bulb and Fuzzy Controller
Electric bulbs use approximately the same power
— independent of any natural or other light source
that is available. If an electric light is on while there are other
light sources, it does not need the same brightness as if it is completely
dark. Therefore, an energy saving light controller that senses light
level and adjusts the bulb’s brightness, by controlling the applied
voltage, may be useful. For a small dwelling, this controller may
not be cost affective, although it could prolong bulb life. In a centralized
control system that lights an entire highrise building, however,
this effort is well worth the cost. Our level of comfort would increase
and the stress to the eye would decrease if the bulbs automatically
adjusted their brightness according to the light available in the
room.
Fuzzy Logic Methodology
These five steps summarize the fuzzy logic methodology:
* Identification of Linguistic Variables
* Defining Linguistic Terms
* Defining the Fuzzy Knowledge Base
* Defining Fuzzy sets for the Linguistic
Terms
* Fuzzy Inference
Identification of Linguistic Variables
Linguistic variables are controlling factors in
a fuzzy
inference mechanism – typically the inputs and outputs.
To identify the linguistic variables we must understand the system
and its intended operation. In our case, the system must sense the
light level in the room and adjust the voltage applied to the bulb.
Therefore, the linguistic variables are Voltage and Light
(the light level in the room  not the light from the bulb). 