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B. Uzun et al.
set into methods such as the fuzzier set or a fuzzy set of crisp sets, respectively. It is
recorded, during the process of fuzzification, the numbers of the inputs or outputs are
changed into fuzzy sets. These fuzzification techniques methods are of two different
ways as defined below:
(a) Support Fuzzification (s-fuzzification) Method:
These fuzzification method is obtainable through the function below:
˜
A = μ 1 Q(x 1 ) + μ 2 Q(x 2 ) + . . . + μ n Q(x n )
(26)
where Q(x i ) denotes the Kernel of fuzzification. This method is also applicable
while keeping μ i as constant and x i as the values converted to a fuzzy set Q(x i ).
(b) Grade Fuzzification (g-fuzzification) Method:
This procedure is nearly comparative to the s-fuzzification strategy with the distinction within the two parameters. In this procedure, x i indicates a constant and μ i
indicates a fuzzy set.
8.4 De-fuzzification
Defuzzification is defined as the method of getting a number obtained from an output
from a fuzzy set. It is utilized to exchange fuzzy interference output. In other words,
defuzzification can be obtained by an algorithm of decision-making that chooses
the finest esteem based on fuzzy set. It is additionally a handle that changes the
fuzzy method into new method. This handle is exceptionally critical for getting a
meaningful output, particularly within the designing applications. De-fuzzification
can be spoken to as “adjusting it off”. The following operations are accessible for
the de-fuzzification:
(a) Max-Membership Method: This procedure is limited to maximum output functions. It is additionally called the height method. It is numerically characterized
as the following equation.
μ ˜
A
x
∗
> μ ˜
A (x), ∀x X
(27)
where x
∗ is the de-fuzzified output.
(b) Centroid Method: This strategy is additionally recognized as center of area
method. The output can be obtained with the equation below:
x
∗
=
∫ μ ˜
A (x) · xdx
∫ μ ˜
A (x) · dx
(28)
B. Uzun et al.
set into methods such as the fuzzier set or a fuzzy set of crisp sets, respectively. It is
recorded, during the process of fuzzification, the numbers of the inputs or outputs are
changed into fuzzy sets. These fuzzification techniques methods are of two different
ways as defined below:
(a) Support Fuzzification (s-fuzzification) Method:
These fuzzification method is obtainable through the function below:
˜
A = μ 1 Q(x 1 ) + μ 2 Q(x 2 ) + . . . + μ n Q(x n )
(26)
where Q(x i ) denotes the Kernel of fuzzification. This method is also applicable
while keeping μ i as constant and x i as the values converted to a fuzzy set Q(x i ).
(b) Grade Fuzzification (g-fuzzification) Method:
This procedure is nearly comparative to the s-fuzzification strategy with the distinction within the two parameters. In this procedure, x i indicates a constant and μ i
indicates a fuzzy set.
8.4 De-fuzzification
Defuzzification is defined as the method of getting a number obtained from an output
from a fuzzy set. It is utilized to exchange fuzzy interference output. In other words,
defuzzification can be obtained by an algorithm of decision-making that chooses
the finest esteem based on fuzzy set. It is additionally a handle that changes the
fuzzy method into new method. This handle is exceptionally critical for getting a
meaningful output, particularly within the designing applications. De-fuzzification
can be spoken to as “adjusting it off”. The following operations are accessible for
the de-fuzzification:
(a) Max-Membership Method: This procedure is limited to maximum output functions. It is additionally called the height method. It is numerically characterized
as the following equation.
μ ˜
A
x
∗
> μ ˜
A (x), ∀x X
(27)
where x
∗ is the de-fuzzified output.
(b) Centroid Method: This strategy is additionally recognized as center of area
method. The output can be obtained with the equation below:
x
∗
=
∫ μ ˜
A (x) · xdx
∫ μ ˜
A (x) · dx
(28)