Main Content


Pi-shaped membership function


This function computes fuzzy membership values using a spline-based pi-shaped membership function. You can also compute this membership function using a fismf object. For more information, see fismf Object.

This membership function is related to the smf and zmf membership functions.


y = pimf(x,params) returns fuzzy membership values computed using a spline-based pi-shaped membership function. This membership function is the product of an smf function and a zmf function, and is given by:


To define the membership function parameters, specify params as the vector [a b c c].

Membership values are computed for each input value in x.


collapse all

Specify input values across the universe of discourse.

x = 0:0.1:10;

Evaluate membership function for the input values.

y = pimf(x,[1 4 5 10]);

Plot the membership function.

title('pimf, P = [1 4 5 10]')
ylabel('Degree of Membership')
ylim([-0.05 1.05])

Input Arguments

collapse all

Input values for which to compute membership values, specified as a scalar or vector.

Membership function parameters, specified as the vector [a b c d]. Parameters a and d define the feet of the membership function, and b and c define its shoulders.

Output Arguments

collapse all

Membership value returned as a scalar or a vector. The dimensions of y match the dimensions of x. Each element of y is the membership value computed for the corresponding element of x.

Alternative Functionality

fismf Object

You can create and evaluate a fismf object that implements the pimf membership function.

mf = fismf("pimf",P);
Y = evalmf(mf,X);

Here, X, P, and Y correspond to the x, params, and y arguments of pimf, respectively.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a

expand all