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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

See also

evalmf, rampmf, trimf, trapmf, sigmf, pimf, psigmf, gaussmf, gbellmf

y = smf(x, a, b)

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

y	Type: Real Description: Degree of membership