# gauss2mf

Gaussian combination membership function

## Description

This function computes fuzzy membership values using a combination of two Gaussian membership functions. You can also compute this membership function using a fismf object. For more information, see fismf Object.

example

y = gauss2mf(x,params) returns fuzzy membership values computed using a combination of two Gaussian membership functions computed. Each Gaussian function defines the shape of one side of the membership function and is given by:

$f\left(x;\sigma ,c\right)={e}^{\frac{-{\left(x-c\right)}^{2}}{2{\sigma }^{2}}}$

To specify the standard deviation, σ, and mean, c, for each Gaussian function, use params.

Membership values are computed for each input value in x.

## Examples

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x = [0:0.1:10]';
y1 = gauss2mf(x,[2 4 1 8]);
y2 = gauss2mf(x,[2 5 1 7]);
y3 = gauss2mf(x,[2 6 1 6]);
y4 = gauss2mf(x,[2 7 1 5]);
y5 = gauss2mf(x,[2 8 1 4]);
plot(x,[y1 y2 y3 y4 y5])

## 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 [σ1 c1 σ2 c2]. Here:

• σ1 and c1 are the standard deviation and mean of the left Gaussian function, respectively.

• σ2 and c2 are the standard deviation and mean of the right Gaussian function, respectively.

When c1c2, the gauss2mf function reaches a maximum value of 1 over the range [c1, c2].

Otherwise, when c1> c2, the maximum value is less than one.

## 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 gauss2mf membership function.

mf = fismf("gauss2mf",P);
Y = evalmf(mf,X);

Here, X, P, and Y correspond to the x, params, and y arguments of gauss2mf, respectively.