functionsigmf
Sigmoidal membership function
Extends from BusinessSimulation.Icons.Function (Icon for functions).
Information
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The function returns the degree of membership using a sigmoid function function given the real input x and the parameters shape parameter to control width of transition area a and center of transition area c.
The sigmoid function will increase from 0 to 1 for positive values of a, while negative values will give rise to a z-shaped transition.
Implementation
y := 1 / (1 + exp(-a * (x - c)));
Syntax
Functions.sigmf(x, a, c);
Examples
Functions.sigmf( 4, a=2, c=4); // 0.5 Functions.sigmf( 2, a=2, c=4); // 0.0179862.. Functions.sigmf( 6, a=2, c=4); // 0.98201379..
See also
evalmf, rampmf, trimf, trapmf, smf, sigmf, pimf, psigmf, gaussmf, gbellmf
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | x | Input value for which the degree of membership is to be computed | |
| Real | a | Shape parameter controlling the width of s-shaped transition area (higher values → steeper transition) | |
| Real | c | Center of the s-shaped transition area |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real | y | Degree of membership |