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<title>Octave Fuzzy Logic Toolkit: gaussmf</title>
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Membership Functions
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Function Reference: <b><code>gaussmf</code></b>
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<dl>
<dt><u>Function File:</u> <var>y</var> = <b>gaussmf</b><i> (<var>x</var>, <var>params</var>)</i></dt>
<dt><u>Function File:</u> <var>y</var> = <b>gaussmf</b><i> (<var>[x1 x2 ... xn]</var>, <var>[sig c]</var>)</i></dt>
</dl>
<p> For a given domain <var>x</var> and parameters <var>params</var> (or <var>[sig c]</var>),
return the corresponding <var>y</var> 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.
</p>
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<p> The argument <var>x</var> must be a real number or a non-empty vector of strictly
increasing real numbers, and <var>sig</var> and <var>c</var> must be real numbers.
This membership function satisfies the equation:
</p>
<pre class="verbatim"> f(x) = exp((-(x - c)^2)/(2 * sig^2))
</pre>
<p> which always returns values in the range [0, 1].
</p>
<p> Just as for the Gaussian (normal) distribution, the parameters <var>sig</var> and
<var>c</var> represent:
</p>
<pre class="verbatim"> sig^2 == the variance (a measure of the width of the curve)
c == the center (the mean; the x value of the peak)
</pre>
<p> For larger values of <var>sig</var>, the curve is flatter, and for smaller values
of sig, the curve is narrower. The <var>y</var> value at the center is always 1:
</p>
<pre class="verbatim"> f(c) == 1
</pre>
<p> To run the demonstration code, type "<tt>demo gaussmf</tt>" (without the quotation
marks) at the Octave prompt.
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<p> <strong>See also: </strong>
<a href="dsigmf.html">dsigmf</a>,
<a href="gauss2mf.html">gauss2mf</a>,
<a href="gbellmf.html">gbellmf</a>,
<a href="pimf.html">pimf</a>,
<a href="psigmf.html">psigmf</a>,
<a href="sigmf.html">sigmf</a>,
<a href="smf.html">smf</a>,
<a href="trapmf.html">trapmf</a>,
<a href="trimf.html">trimf</a>,
<a href="zmf.html">zmf</a>
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Example: 1
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<td> </td>
<td><pre class="example">
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;
</pre></td></tr></tbody>
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