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). 