gaussmf

Gaussian membership function

Syntax

y = gaussmf(x,params)

Description

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:

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

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

Membership values are computed for each input value in x.

Examples

Gaussian Membership Function

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.

plot(x,y)
xlabel('gaussmf, P=[2 5]')
ylabel('Membership')
ylim([-0.05 1.05])

Input Arguments

x — Input values

scalar | vector

Input values for which to compute membership values, specified as a scalar or vector.

params — Membership function parameters

vector of length two

Membership function parameters, specified as the vector [σ c], where σ is the standard deviation and c is the mean.

Output Arguments

y — Membership value

scalar | vector

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

R2018b: C and C++ code generation support

This function supports C and C++ code generation using MATLAB^® Coder™.