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Gaussian membership function


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

A Gaussian membership function is not the same as a Gaussian probability distribution. For example, a Gaussian membership function always has a maximum value of 1. For more information on Gaussian probability distributions, see Normal Distribution (Statistics and Machine Learning Toolbox).


y = gaussmf(x,params) returns fuzzy membership values computed using the following Gaussian membership function:


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

Membership values are computed for each input value in x.


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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 = gaussmf(x,[2 5]);

Plot the membership function.

xlabel('gaussmf, P=[2 5]')
ylim([-0.05 1.05])

Figure contains an axes object. The axes object contains an object of type line.

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 [σ c], where σ is the standard deviation and c is the mean.

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 gaussmf membership function.

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

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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Version History

Introduced before R2006a