gauss2mf

Gaussian combination membership function

collapse all in page

Syntax

y = gauss2mf(x,params)

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.

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(x;σ,c)=e−(x−c)22σ2

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.

example

Examples

collapse all

Open Live Script

Specify input values across the universe of discourse.

x = 0:0.1:10;

Evaluate several membership functions for the input values.

y1 = gauss2mf(x,[2 4 1 8]);
y2 = gauss2mf(x,[2 5 1 7]);
y3 = gauss2mf(x,[2 6 1 6]);

Plot the membership function.

plot(x,y1,x,y2,x,y3)
xlabel("x")
ylabel("Degree of Membership")
ylim([-0.05 1.05])
legend("P = [2 4 1 8]","P = [2 5 1 7]","P = [2 6 1 6]",...
    Location="northwest")

Figure contains an axes object. The axes object with xlabel x, ylabel Degree of Membership contains 3 objects of type line. These objects represent P = [2 4 1 8], P = [2 5 1 7], P = [2 6 1 6].

Input Arguments

collapse all

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 c1 ≤ c2, 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

collapse all

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.

Extended Capabilities

expand all

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

Version History

Introduced before R2006a

expand all

See Also

| | | | | | | | | | |

Topics