functionsmf

S-shaped membership function

Extends from BusinessSimulation.Icons.Function (Icon for functions).

Information

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The function returns the degree of membership using a S-shaped function given the real input x and the parameters foot a and shoulder b of the function.

Implementation

  y := if x <= a then 0
    elseif a < x and x <= midpoint then 2 * ( (x-a)/(b-a) )^2
    elseif midpoint < x and x <= b then 1 - 2 * ( (x-b)/(b-a) )^2
    else 1;

Syntax

Functions.smf(x, a, b);

Examples


Functions.smf( 5, a=2, b=8); // 0.5
Functions.smf( 1, a=2, b=8); // 0.0
Functions.smf( 9, a=2, b=8); // 1.0

Inputs

Type	Name	Description
Real	x	Input value for which the degree of membership is to be computed
Real	a	Foot of the function (i.e., f(a) = 0)
Real	b	Shoulder of the function (i.e., f(b) = 1)

Outputs

Type	Name	Default	Description
Real	y		Degree of membership