Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Logical Operators and Fuzzy Operators:
Fuzzy logic is an extension of the standard logic and it can be used the
same logical operators such as AND, OR and NOT with fuzzy logic, but with
the expansion of the concept of some of these factors in order to serve fuzzy
logic. The difference between the logical operators and fuzzy factors in the
recent, run on the two numbers 0 and 1 as well as decimals confined between
them, so these factors should be used in a way that fuzzy logic expands the
concept of classical logic while preserving the principle of work and truth
tables. The following figure shows the relationship between the logical factors
and fuzzy factors.
The relationship between the logical factors and the fuzzy factors.
A simple reading of the truth table logical function AND can be inferred that
this process choose less element of their transactions, so you can expand the
AND logic to fuzzy AND using min which returns smaller factors, the logical
function OR is always return largest factors and it can fuzzification logical OR
using max function that returns the largest factors. the logical NOT function can
be obtained by taking complement of NOT. Former figure shows that the
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Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
logical factors and fuzzy factors given the same results when applied to binary
numbers.
Fuzzy Rules:
Aggregates and fuzzy factors are used for building and formulate a set of
conditional sentences that takes the formula (If - Then).
2.1 Fuzzy Rule Formulation:
Fuzzy Rule formulated as follows:
If x is A Then y is B
Where each of A and B represents the fuzzy sets has ranges of cosmic X and Y,
respectively. Called part If (x is A) as Antecedent or Premise while Then (y is B)
is called the Consequence or Conclusion, but the word is contained in the Fuzzy
Rule serve as belonge to ∊. It can be part of the Premise that consists of a set of
connection conditions and linking them fuzzy factors as follows:
If (x1 is A1) AND (x2 is A2) AND … AND (xn is An) Then y is B
Where A1 .. An represent fuzzy sets, and can use the OR or NOT in the Premise
fuzzy rules. Conclusion part may contain multiple conclusions as follows:
If (x1 is A1) AND (x2 is A2) AND … AND (xn is An) Then (y1 is B1) AND
(y2 is B2) AND …AND (ym is Bm)
2.2 Strength Of Rule:
Rule strength represents the value of truth Premise conditions offered to
and a way to find rule strength depends on the type of fuzzy factors that link the
among Premise conditions. In the beginning, it is replaced every clause in the
Premise with its own membership degree, in other words, the fuzzy base if x is
A then y is B is converted to the following:
x is A
convert to
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µA (x)
Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Where μA (x) is the membership degree of element x in the fuzzy set A
that is obtained by applying membership function law representing the fuzzy
value of A, and after the replacement procedure is done , the truth value of a
whole Premise has been found and here comes the role of fuzzy factor that
connects the parts. The following example shows how to find the strength of the
fuzzy rule:
Example: Find Strength of The Following Fuzzy Rule:
If (v1 is High) AND (v2 is Low) Then y = 5
where the input variables v1 = 4 , v2 = 6 and membership function shows as
follows
To compute strength of rule, computing membership degree using trapzoidal
equation as follows:
First: detemine operators of each function on the universe of discourse:
a
b c
d
‫ـــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــــ‬
v1 (high)
3 8 10 10
v2 (low)
1 1 4 8
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Babylon University- Science College for Women- Advanced Intelligent App.
4th Class
Fuzzy System
M.S.C.: Zainab Falah
Second : apply the following equation directly:
4-3
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µ high (v1) = ‫ = ــــــ = ـــــــــــــ‬0.2
8-3
5
8-6 = ‫ــــــ‬
2 = 0.5
µ low (v2) = ‫ــــــــــــــ‬
8-4
4
v1 is High is replaced by value (0.2)and v2 is Low by value (0.5), while AND
connect the premise parts then truth value "if (v1 is High) and (v2 is Low)" is
smallest membership degree in the premise that represents strength of rule:
Strength of rule = Min (0.2 , 0.5) = 0.2
Next lecture spooler:
we will learn how to evaluate the conclusion part , implication of fuzzy rules , the types of
fuzzy systems and the difference between them.
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