There are other type of membership functions in fuzzy logic like Bell, Sigmoidal, Asymmetric , L-R etc. But only Guassian, Triangular and trapezoidal MF are used in fuzzy ARM. What is the reason behind it ?
We often use triangular and trapezoidal membership function because, calculations with triangular and trapezoidal membership are easy. We can not easily calculate the arithmetic operations in case of Bell, Sigmoidal, Asymmetric , LR, Guassian,
Hello, I agree with opinion of Pushpinder Singh and I would like to add something:
Advantages of polygonal membership functions:
1. a small amount of data is needed to define the membership function,
2. easy of modification of parameters (modal values) of membership functions on the basis of measured values of the input --> output of a system,
3. the possibility of obtaining input --> output mapping of a model which is a hypersurface consisting of linear segments,
4. polygonal membership functions mean the condition of a partition of unity (it means that the sum of membership grades for each value x amounts to 1) is easily satisfied.
Disadvantages of polygonal membership functions:
1. Polygonal membership functions are not continuously differentiable.
The main disadvantage of other membership functions is fact, that majority of other membership functions are usually symmetric and it means that the sum of membership grades for each value x doesn't everytime amount to 1. Additionally, these functions are much harder to identification.
The usage of trapmf or trimf are depends on your application or controlling system. but according to my research and knowledge in this field, these shapes are simple and more flexible. but you must to check your input data and controlling system befor choosing membership function generators. so choosing memberships, requres expert knowledges.
Since triangular membership function are fewer complexes when splitting values (low, med and high MF) comparing other membership functions.
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