smf

S-shaped membership function

Syntax

y = smf(x,[a b]) 

Description

This spline-based curve is a mapping on the vector x, and is named because of its S-shape. The parameters a and b locate the extremes of the sloped portion of the curve, as given by:

f(x;a,b)={0,xa2(xaba)2,axa+b21-2(xbb-a)2,a+b2xb1,xb}

Examples

expand all

S-Shaped Membership Function

x = 0:0.1:10;
y = smf(x,[1 8]);
plot(x,y)
xlabel('smf, P=[1 8]')
ylim([-0.05 1.05])

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