Flex.MembershipFun (FLex v0.2.2)
View SourceAn interface to create Membership Functions reference.
Summary
Functions
Gaussian membership derivatived function.
Generalized Bell membership derivatived function.
An interface to execute derivatives of membership functions, where,
Gaussian membership function.
Generalized Bell membership function.
For Takagi-Sugeno-Kang fuzzy inference, uses this output membership functions that are either constant or a linear function that will be combined with the input values.
Pi-shaped membership function.
S-shaped membership function.
Saturation membership function.
Shoulder membership function.
Sigmoidal membership function.
Trapezoidal membership function.
Triangle membership function.
Z-shaped membership function.
Functions
Gaussian membership derivatived function.
m
- (number) Mean,s
- (number) Standard deviation, it must not be equal to 0.f
- (number) Fuzzification Factor.mu
- (number) Last membership function value.
Generalized Bell membership derivatived function.
c
- (number) Center.s
- (number) Slope.b
- (number) The width of the curve, it must not be equal to 0.
Definition of Generalized Bell function is:
y(x) = 1 / (1 + |((x - c) / b)|^(2 * s))
An interface to execute derivatives of membership functions, where,
z_i
- is the i'th rule output.x, y
- are the values of input 1 and input 2, respectively.a_i, b_i, and c_i
- are constant coefficients of the i'th rule output. For a zero-order Takagi-Sugeno system, z_i is a constant (a = b = 0).
Gaussian membership function.
m
- (number) Mean,s
- (number) Standard deviation, it must not be equal to 0.f
- (number) Fuzzification Factor,
Generalized Bell membership function.
c
- (number) Center.s
- (number) Slope.b
- (number) The width of the curve, it must not be equal to 0.
Definition of Generalized Bell function is:
y(x) = 1 / (1 + |((x - c) / b)|^(2 * s))
@spec linear_combination([...]) :: {fun(), nil}
For Takagi-Sugeno-Kang fuzzy inference, uses this output membership functions that are either constant or a linear function that will be combined with the input values.
Example (2 inputs 1 output): z_i = a_ix + b_iy + c_i
where,
z_i
- is the i'th rule output.x, y
- are the values of input 1 and input 2, respectively.a_i, b_i, and c_i
- are constant coefficients of the i'th rule output. For a zero-order Takagi-Sugeno system, z_i is a constant (a = b = 0).
## Example (in Elixir)
iex> {z_i_mf, nil} = MembershipFun.linear_combination([a_i, b_i, c_i])
iex> z_i = z_i_mf.([x,y])
Pi-shaped membership function.
S-shaped membership function.
Saturation membership function.
Shoulder membership function.
Sigmoidal membership function.
c
- (number) Crossover point.s
- (number) Slope.
Definition of Generalized Bell function is:
y(x) = 1 / (1 + e^(-s(x-c)))
Trapezoidal membership function.
Triangle membership function.
Z-shaped membership function.