# linzmf

Linear z-shaped saturation membership function

## Description

This function computes fuzzy membership values using a linear z-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 trimf, trapmf, and linsmf membership functions.

example

y = linzmf(x,params) returns fuzzy membership values computed using a linear z-shaped saturation membership function.

• When a < b:

$f\left(x;a,b\right)=\left\{\begin{array}{ll}1,\hfill & xb\hfill \end{array}\right\}$

• When a = b:

$f\left(x;a,b\right)=\left\{\begin{array}{cc}1,& x

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

Membership values are computed for each input value in x.

## Examples

collapse all

Specify input values across the universe of discourse.

x = 0:0.1:10;

Evaluate a linear z-shaped membership function for the input values.

y = linzmf(x,[4 6]);

Plot the membership function.

plot(x,y)
xlabel('linzmf, P = [4 6]')
ylabel('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]. Parameter a defines the shoulder of the membership function, and b defines its foot. Setting a equal to b produces a crisp membership function.

## 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 linsmf membership function.

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

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

## Version History

Introduced in R2022a