The use of neural networks in fuzzy modelling and control systems which are built on fuzzy logic has made possible the creation of the so-called neuro-fuzzy systems.
A neuro-fuzzy system is a modified artificial neural network, meaning that this system contains a fuzzy system and more memory storage capacities than a simple neural network. Fuzzy systems are considered to be more friendly than neural networks because their behaviour can be explained using the human reasoning model. The main feature of a fuzzy system is that it can control data related to the vocabulary of a language and numerical data as well (Full 1995).
The process of a fuzzy system involves the transformation of the input data, described by a non-linear function-given by …show more content…
Remark:
The following IF-THEN rules have been considered:
IF u_1 is H_1^p and…and H_n^p THEN y is F^P, where p={1,2,…,P}
Fuzzy logic
Fuzzy logic involves set membership and according to the set theory, an object can either be an element of a set or not be its element. Otherwise, is a paradox which can be illustrated with the below example.
Example 3.1
The degree of membership for a 5 feet woman to the short stature set is 0.7. So, we can deduce that the degree of membership for this woman to the tall stature set is 0.3. According to the set theory, this means that the woman is simultaneously an element of the two sets.
Starting from the mathematical logic, which involves defining a membership function to a set M: g^m (x) ∈{0,1} we have:
-if g^m (x)=0, then x∉ M;
-if g^m (x)=1, then x ∈ M;
But, if we apply fuzzy logic to g^m (x), the function is:
g^m (x) ∈
A neuro-fuzzy system is a modified artificial neural network, meaning that this system contains a fuzzy system and more memory storage capacities than a simple neural network. Fuzzy systems are considered to be more friendly than neural networks because their behaviour can be explained using the human reasoning model. The main feature of a fuzzy system is that it can control data related to the vocabulary of a language and numerical data as well (Full 1995).
The process of a fuzzy system involves the transformation of the input data, described by a non-linear function-given by …show more content…
Remark:
The following IF-THEN rules have been considered:
IF u_1 is H_1^p and…and H_n^p THEN y is F^P, where p={1,2,…,P}
Fuzzy logic
Fuzzy logic involves set membership and according to the set theory, an object can either be an element of a set or not be its element. Otherwise, is a paradox which can be illustrated with the below example.
Example 3.1
The degree of membership for a 5 feet woman to the short stature set is 0.7. So, we can deduce that the degree of membership for this woman to the tall stature set is 0.3. According to the set theory, this means that the woman is simultaneously an element of the two sets.
Starting from the mathematical logic, which involves defining a membership function to a set M: g^m (x) ∈{0,1} we have:
-if g^m (x)=0, then x∉ M;
-if g^m (x)=1, then x ∈ M;
But, if we apply fuzzy logic to g^m (x), the function is:
g^m (x) ∈