# sigmf

Sigmoidal membership function

## Description

This function computes fuzzy membership values using a sigmoidal 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 dsigmf and psigmf membership functions.

example

y = sigmf(x,params) returns fuzzy membership values computed using the sigmoidal membership function given by:

$\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}f\left(x;{a}_{k},{c}_{k}\right)=\frac{1}{1+{e}^{-{a}_{k}\left(x-{c}_{k}\right)}}$

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

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 membership function for the input values.

y = sigmf(x,[2 4]);

Plot the membership function.

plot(x,y)
title('sigmf, P = [2 4]')
xlabel('x')
ylabel('Degree of 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 c]. To open the membership function to the left or right, specify a negative or positive value for a, respectively. The magnitude of a controls the width of the transition area, and c defines the center of the transition area.

## 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 sigmf membership function.

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

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

## Version History

Introduced before R2006a

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