Documentation

sigmf

Sigmoidal membership function

Description

This function computes fuzzy membership values using the difference between two sigmoidal membership functions. 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:

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

To specify the a and c parameters, use params.

Membership values are computed for each input value in x.

Examples

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x = 0:0.1:10;
y = sigmf(x,[2 4]);
plot(x,y)
xlabel('sigmf, P = [2 4]')
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.