5.12 Fuzzy ControL SySteM 145
Figure 5.14 shows fuzzy rules and their relationship in the portfolio
management for a financial application (Sajja, 2006).
5.12 FUZZY CONTROL SYSTEM
A fuzzy control system is based on fuzzy logic. Given membership func-
tions that map crisp values to fuzzy values and vice versa, the machine can
interact with the human being in friendlier way. Fuzzy logic systems address
the imprecision of the input and output variables by defining fuzzy numbers
and fuzzy sets, which can be expressed in linguistic variables (e.g., high, low,
and average). Fuzzy controllers are the most important applications of fuzzy
theory. They work rather differently from conventional controllers because
the experts’ knowledge is used for more effective and human-like control
instead of a pure, crisp, mathematical approach (like differential equations)
to describe a system.
This knowledge can be expressed in a natural way using linguistic variables,
which are described by fuzzy sets. Fuzzy logic-based control systems are also
useful for some of the control applications where a systematic mathematical
model does not exist. Instead of describing control strategy as mathematical
equations, control is expressed as a set of linguistic rules. A control system can
be abstracted as a box with inputs flowing into it and outputs emerging from
Figure 5.14
Fuzzy rules and
relationships
510152025303540
20
40
60
80
100
120
1
0.5
0
0 0.5 1
Less Moderate More
Low
Average
High
Investment amount in thousands
If profit is high
then invest more
Profit in percentage
Membership
degree
Membership degree
76473_CH05_Akerkar.indd 145 8/11/09 10:16:58 AM
146 Chapter 5 Fuzzy LogiC
it. The process of designing a fuzzy control system can be described using fol-
lowing steps:
Step 1: Identify the principal input, output, and process tasks.
Step 2: Identify linguistic variables used, and define fuzzy sets and mem-
bership accordingly.
Step 3: Use these fuzzy sets and linguistic variables to form procedural
rules.
Step 4: Determine the defuzzification method.
Step 5: Test the system and modify if necessary.
The components of a typical control system are shown in Figure 5.15.
Mamdani and Assilian (1975) designed a fuzzy control system for a
steam engine. The purpose was to maintain a constant speed by control-
ling the pressure on pistons by adjusting the heat supplied to a boiler. After
that, fuzzy controllers were developed for air conditioners, video cameras,
washing machines, and so on. The fuzzy control system can be considered a
nonlinear static function that maps controller inputs on controller outputs.
Fuzzy controllers are used for systems where a preferred response must be
maintained based on whatever inputs are received. Naturally, inputs to the
system can alter the state of the system, which causes a change in response.
Thus, the duty of the controller is to take appropriate action by providing a
set of inputs to ensure the preferred response.
A fuzzy controller consists of four main components:
Fuzzy knowledge base: The knowledge base consists of fuzzy rules for 1.
the system that represent the knowledge and experience of a human
expert. For example, “If the temperature is fairly high and the pressure is
very low, then the output is medium.
Figure 5.15
A fuzzy controller
Output
Input
Process
Fuzzy
rules
Fuzzy sets and
definitions of
membership
functions
User
interface
Machine
interface
Fuzzy values for
human interface
Crisp values for
machine interface
Interpretation
User
Instrument
76473_CH05_Akerkar.indd 146 8/11/09 10:16:58 AM

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