Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Fuzzy logic:
Fuzzy logic is a form of many-valued logic in which the truth values of
variables may be any real number between 0 and 1. By contrast, in Boolean
logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been
extended to handle the concept of partial truth, where the truth value may range
between completely true and completely false.
The term fuzzy logic was introduced with the 1965 proposal of fuzzy set
theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from
control theory to artificial intelligence.
Fuzzy Logic Algorithm:
1. Define the linguistic variables and terms (initialization)
2. Construct the membership functions (initialization)
3. Construct the rule base (initialization)
4. Convert crisp input data to fuzzy values
5. Using the membership functions (fuzzification)
6. Evaluate the rules in the rule base (inference)
7. Combine the results of each rule (inference)
8. Convert the output data to non-fuzzy values (defuzzification)
Why fuzzy logic:
 Ease of understand: mathmatical concepts that fuzzy logic depend on is
simple.
 Flexibility: in any fuzzy system, set of additional functions can added
without needed to rebuild of system newly.
 Appility to deal with imprecise data efficiently: in real world, every thing
appears imprecise even check it carefully, fuzzy logic is characterized by
its ability to deal with the lack of precision and get very good results
using inaccurate data
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Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
 Fuzzy logic depend on natural language: fuzzy logic depend on natural
language used in human communication support, making it easy to use.
 Fuzzy logic can simulate nonlinear function with high complixity: it can
build fuzzy system to matching any set(input_output) , especially with
appearing powerful technologies such as (ANFIS) and are systems
merged fuzzy logic with artificial neural networks.
Fuzzy Sets and classical set:
Classical set theory based on the principle of excluded middle which was
formulated for the first time at the hands of the Greek philosopher Aristotle and
which stipulates that the element x either belongs to a group A or does not
belong to them and therefore, the expression of membership of an item and
belonging to the group will likely one things: (yes, no), (true, false), (1,0) which
makes this a binary logic value (Two-Valued) and does not allow the existence
of compromises.
In the real world it seems to be different, man expresses things using
fuzzy words carry a great deal of possibilities, for example: to express the
length of the human person uses words such as: (long, short, too long, too short,
medium height) and But binary logic value fails to represent all of these spectra.
As a result of the limited possibilities of the binary logic value, the applicability
in the practical life is limited to simple applications and limited from here and
needed to find an alternative to this logic was fuzzy set Theory.
Fuzzy set theory came in order to ease the severe restrictions imposed by
the classical set theory, The expression of membership of an item in the fuzzy
set theory can take multiple possibilities are:
• element belonging to the set were certain.
• element does not belong to the group at all.
• element belongs to the group in part or in other words, a certain degree.
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Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Linguistic Variables:
The brain of human can explain imprecise and incompelete information
supplied by the senses Owned , and the pursuit of human simulation in his
behavior and his actions came fuzzy logic to be a way to account using words
instead of numbers, for example, you can express the heat by using words such
as very cold, cold, very hot, hot, warm in 1973 suggested Professor Lotfi Zadeh
of the concept of linguistic variables, and with the words less accurate than the
numbers, however, there are many motives that justify their use as an alternative
to numbers including:
 Use ward is nearest to human intuition.
 Computation use ward instead of numbers can deal efficiently with the
levels of imprecise, so it is reduce the solution complexity
Linguistic variables are the input or output variables of the system whose
values are words or sentences from a natural language, instead of numerical
values. A linguistic variable is generally decomposed into a set of linguistic
terms.
Every linguistic variable has the following properties
Universe of discourse:
The universe of discourse in which the fuzzy sets are defined to the
domain of the system input and output variables. Universe of discourse is
refered as (UOD) which is represent the real inputs of the fuzzy system.
Fuzzy Value:
The universe of discourse is divided into parts and sub-ranges can
interfere with each other, and each part is given over the name expresses the
properties appear in language use, such as large, Medium, Negative and these
names are also known Linguistic values, Labels or sets
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Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Membership Functions:
A membership function (MF) is a curve that defines how each point in the
input space is mapped to a membership value (or degree of membership)
between 0 and 1. The input space is sometimes referred to as the universe of
discourse, a fancy name for a simple concept.
Membership functions are used in the fuzzification and defuzzification
steps of a FLS, to map the non-fuzzy input values to fuzzy linguistic terms and
vice versa. A membership function is used to quantify a linguistic term.
Fig. 1: Computation of Membership Degree
This figure shows that fuzzy variable has the following properties:
 Universe of discourse from 1 to 10 .
 One fuzzy value called fat.
 Trapezoidal membership function is used to represent fuzzy value fat.
This figure shows that membership degree of 7 is 0.5 , where the value 7 cross
with membership function in y -Coordinate point is 0.5
Next lecture spooler:
After we learned that the key terms of logic and fuzzy membership function calculation
method for an item by drawing, in the next lecture, you will learn about the way the
membership function of any component in the Universe of discourse mathematically.
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