Fuzzy Logic Approach - Computational Intelligence in Time Series Forecasting - page 143

x in specification of system parameters
x in representation of input, output and system states.

When involved in system description, fuzzy sets appear as linguistic terms or
labels to represent the state of the linguistic variable in the fuzzy rule. An
illustration of the first case can be presented considering once again Boyle's
observations, which are described by three IF-THEN rules, as stated in the Section
4.2. In fact, any system can be described by a collection of such types of IF-THEN
linguistic rules, also known as fuzzy rules. The fuzzy logic systems are actually a
rule-based system and usually defined using the IF-THEN rules. The general form
of such an IF-THEN rule is: IF antecedent propositions THEN consequent
propositions . The example of fuzzy (antecedent) propositions can be “ Pressure is
High ” or even “ x is A ”. Here, the term “ High ” is a linguistic term or label, also
called a fuzzy term, represented by a fuzzy set (membership function) on the
universe of discourse (UD) of the linguistic variable “Pressure”. Similarly, fuzzy
set A is a representative of a linguistic label/term. Sometimes linguistic hedges
(modifier) are used to modify the linguistic label/fuzzy set without redefining the
fuzzy set completely. An example of the latter can be “very A ” or “more or less A ,”
etc .

When involved in specification of system parameters, fuzzy sets may appear as
fuzzy numbers. Similarly, as an example of the second case, let us consider a
system that can be described by algebraic or differential equations in which the
parameters are approximate (fuzzy) numbers instead of exact real numbers. For
instance, a linear system of the form

, where x is the input to the system
and y is the corresponding output from the system, can be represented by a linear
equation, but one with fuzzy numbers such as

yf x

, where the numbers 2
and 3 (with tilde symbol) represent the fuzzy numbers approximately 2 and
approximately 3 respectively.
Finally, fuzzy sets may appear as the only means to express human perceptions
or even noisy or uncertain data or information that have to be used as system input,
output, and system state. As an illustration of the latter, consider the input of a
system that can be noisy data (reading from unreliable sensors/transducers), or
even human perceptions such as hot, warm, comfortable, uncomfortable, beautiful,
and tasty, etc . Fuzzy-logic-based system can process such types of information by
defining their suitable ranges and criteria with fuzzy sets.
A fuzzy inference system is the core part of a fuzzy logic system. In practice,
the following fuzzy inference systems have most frequently been employed and
have most frequently been the subject of theoretical study:

yx 2 3

x Mamdani type fuzzy inference systems
x Takagi-Sugeno type fuzzy inference systems
x Relational (Pedrycz) fuzzy logic systems.