For a given domain x and parameters params (or [sig c]), return the corresponding y values for the Gaussian membership function. This membership function is shaped like the Gaussian (normal) distribution, but scaled to have a maximum value of 1. By contrast, the area under the Gaussian distribution curve is 1.
The argument x must be a real number or a non-empty vector of strictly increasing real numbers, and sig and c must be real numbers. This membership function satisfies the equation:
f(x) = exp((-(x - c)^2)/(2 * sig^2))
which always returns values in the range [0, 1].
Just as for the Gaussian (normal) distribution, the parameters sig and c represent:
For larger values of sig, the curve is flatter, and for smaller values of sig, the curve is narrower. The y value at the center is always 1:
To run the demonstration code, type demo('gaussmf') at the Octave prompt.
See also: dsigmf, gauss2mf, gbellmf, pimf, psigmf, sigmf, smf, trapmf, trimf, zmf.
The following code
x = -5:0.1:5; params = [0.5 0]; y1 = gaussmf(x, params); params = [1 0]; y2 = gaussmf(x, params); params = [2 0]; y3 = gaussmf(x, params); figure('NumberTitle', 'off', 'Name', 'gaussmf demo'); plot(x, y1, 'r;params = [0.5 0];', 'LineWidth', 2); hold on ; plot(x, y2, 'b;params = [1 0];', 'LineWidth', 2); hold on ; plot(x, y3, 'g;params = [2 0];', 'LineWidth', 2); ylim([-0.1 1.1]); xlabel('Crisp Input Value'); ylabel('Degree of Membership'); grid; hold;
Produces the following figure
Figure 1 |
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Package: fuzzy-logic-toolkit