Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 142

The same fact can be written mathematically as PV = constant.
The above three IF-THEN rules are sufficient to model Boyle's observations
and is in fact very similar to the way we understand a system or describe our
observations and experience about any system in day-to-day life. In the above three
rules, pressure, temperature and volume are the linguistic variables, whereas ( fuzzy
sets ) high, medium, low, etc. are the linguistic terms or linguistic labels, generally
represented by triangular or trapezoidal or even by Gaussian membership
functions (fuzzy sets) .
For example, in the above rules, say 0.9 to 1.5 bar represents high pressure, 0.4
to 1.0 bar represents medium pressure and 0 to 0.5 bar represents low pressure, etc.
Note that, here, instead of exact and specific values of pressure we used a range to
specify high, low and medium, and also note that ranges are partially overlapping.
So, from the above example it is clear that fuzzy logic (IF-THEN linguistic
rules) is a very convenient mathematical tool to describe our observations or
experiences about any system for system modelling with the application of fuzzy
sets.

4.3 Fuzzy Logic Systems

Fuzzy logic systems have a direct relationship with fuzzy concepts, such as fuzzy
sets, linguistic variables, and fuzzy logic. Fuzzy systems are unique in the sense
that they can simultaneously process numerical data and linguistic knowledge.
From the mathematical point of view, a fuzzy logic system is a nonlinear mapping
of an input feature (data) vector into a scalar output.

Crisp
input
X

Crisp
output
Y

Fuzzy
inference
engine

Fuzzifier Defuzzifier

Fuzzy
rule base

Figure 4.2. Block diagram of a fuzzy logic system

The block diagram of a fuzzy logic system is shown in Figure 4.2. From the figure
it is seen that the fuzzy logic system takes the crisp input value ( X ) and this is then
fuzzified (converted into corresponding membership grade in the input fuzzy sets),
thereafter, it is fed to the fuzzy inference engine. Using the stored IF-THEN fuzzy
rules from the rule base the inference engine produces a fuzzy output that
undergoes further defuzzification to result in crisp output ( Y ).
In artificial intelligence, fuzzy logic systems were first styled as fuzzy rule
systems and fuzzy expert systems .
Fuzzy sets can be involved in a fuzzy logic system in a number of ways:

x in system description