Fuzzy Membership Functions
Inputs and outputs of Mamdani type and Inputs of
Sugeno type can be chosen from 11 member functions.
1. dsigmf: Composed of
different between two spline curves, See Fig 1.
2. gauss2mf: Gaussian
combination, See Fig 2.
3. gaussmf: Gaussian curve,
See Fig 3.
4. gbellmf: Generalized
bell-shape, See Fig 4.
5. pimf: -shape, See Fig 5.
6. psigmf: Composed of
product of two Sigmoidally shaped mf, See Fig 6.
7. sigmf: Sigmoidally shape,
See Fig 7.
8. smf: Spline-based curve ,
See Fig 8.
9. trapmf: Trapezoidal-shape,
See Fig 9.
10.
trimf: Triangular shape, See Fig 10.
11.
zmf: Z-shape, See Fig 11.
Each member function and required parameters are described in
Table 1.
|
No. |
Name |
Number of Parameter |
Mathematical definition |
|
1 |
dsigmf |
4 |
about arbitrary x
MF Parameters a1,c1,a2 and c2 |
|
2 |
gauss2mf |
4 |
about arbitrary x
MF Parameters sig1 , c1, sig2, and c2
If c1 < c2, the maximum value is 1. |
|
3 |
gaussmf |
2 |
about arbitrary x
MF Parameters sig and c |
|
4 |
gbellmf |
3 |
about arbitrary x
MF Parameters a, b and c |
|
5 |
pimf |
4 |
about arbitrary x
MF Parameters a,b,c and d |
|
6 |
psigmf |
4 |
about arbitrary x
MF Parameters a1, c1,a2 and c2 |
|
7 |
sigmf |
2 |
about arbitrary x
MF Parameters a and c |
|
8 |
smf |
2 |
about arbitrary x
MF Parameters a and b |
|
9 |
trapmf |
4 |
about arbitrary x
MF Parameters a, b, c and d |
|
10 |
trimf |
3 |
about arbitrary x
MF Parameters a, b and c |
|
11 |
zmf |
2 |
about arbitrary x
MF Parameters a and b |
Table 1 Member functions in Fuzzy logic
Figure 1 'dsigmf'
Membership Function
Figure 2 'gauss2mf'
Membership Function
Figure 3 'gaussmf'
Membership Function
Figure 4 'gbellmf'
Membership Function
Figure 5 'pimf' Membership
Function
Figure 6 'psigmf'
Membership Function
Figure 7 'sigmf'
Membership Function
Figure 8 'smf' Membership
Function
Figure 9 'trapmf'
Membership Function
Figure 10 'trimf'
Membership Function
Figure 11 'zmf' Membership
Function
Output member functions of Sugeno type is two.
Actually this member functions (MFs) is related Fuzzy rule of
Sugeno type. The parameters of this MFs are consists of a value of
linear first order polynomial equation including input numbers. Therefore, the
number of parameters is the number of inputs plus 1.
•
constant: one of a linear type that just has zero coefficient of
first order value.
•
linear: for example '
'. The numbers of
parameters are n. The number of inputs is n-1. The constant value is a0.