pimf

Π-shaped membership function

Syntax

y = pimf(x,[a b c d]) 

Description

This spline-based curve is so named because of its Π shape. The membership function is evaluated at the points determined by the vector x. The parameters a and d locate the "feet" of the curve, while b and c locate its "shoulders." The membership function is a product of smf and zmf membership functions, and is given by:

f(x;a,b,c,d)={0,xa2(xaba)2,axa+b212(xbb-a)2,a+b2xb1,bxc12(xcdc)2,   cxc+d2   2(xdd-c)2,     c+d2xd          0,                    xd}

Examples

expand all

Pi-Shaped Membership Function

x = 0:0.1:10;
y = pimf(x,[1 4 5 10]);
plot(x,y)
xlabel('pimf, P=[1 4 5 10]')
ylim([-0.05 1.05])

Was this topic helpful?