This information is part of the Business Simulation Library (BSL). Please support this work and ► donate.

The function returns the degree of membership using a Pi-shaped function given the real input x and the parameters foot of the s-shaped part a, shoulder of the s-shaped part b, shoulder of the z-shaped part c, and foot of the z-shaped part d of the function.

Implementation

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

Syntax

Functions.pimf(x, a, b, c, d);

Examples

Functions.pimf(   5, a=1, b=4, c=5, d=10); // 1.0
Functions.pimf( 2.5, a=1, b=4, c=5, d=10); // 0.5
Functions.pimf(   1, a=1, b=4, c=5, d=10); // 0.0
Functions.pimf( 7.5, a=1, b=4, c=5, d=10); // 0.5
Functions.pimf(  10, a=1, b=4, c=5, d=10); // 0.0

See also

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

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

x	Type: Real Description: Input value for which the degree of membership is to be computed
a	Type: Real Description: Foot of the s-shaped part(lower bound of the support)
b	Type: Real Description: Shoulder of the s-haped part (lower bound of the core)
c	Type: Real Description: Shoulder of the z-shaped part (upper bound of the core)
d	Type: Real Description: Foot of the z-shaped part (upper bound of the support)

y	Type: Real Description: Degree of membership