# linsmf

Linear s-shaped saturation membership function

## Description

This function computes fuzzy membership values using a linear s-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 linzmf membership functions.

example

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

• When a < b:

$f\left(x;a,b\right)=\left\{\begin{array}{ll}0,\hfill & xb\hfill \end{array}\right\}$

• When a = b:

$f\left(x;a,b\right)=\left\{\begin{array}{cc}0,& 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

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Specify input values across the universe of discourse.

x = 0:0.1:10;

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

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

Plot the membership function.

plot(x,y)
xlabel('linsmf, P = [4 6]')
ylabel('Membership')
ylim([-0.05 1.05])

## Input Arguments

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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 foot of the membership function, and b defines its shoulder. Setting a equal to b produces a crisp membership function.

## Output Arguments

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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("linsmf",P);
Y = evalmf(mf,X);

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

## Version History

Introduced in R2022a