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<title>Octave Fuzzy Logic Toolkit: gauss2mf</title>
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Membership Functions
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Function Reference: <b><code>gauss2mf</code></b>
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<dl>
<dt><u>Function File:</u> <var>y</var> = <b>gauss2mf</b><i> (<var>x</var>, <var>params</var>)</i></dt>
<dt><u>Function File:</u> <var>y</var> = <b>gauss2mf</b><i> (<var>[x1 x2 ... xn]</var>, <var>[sig1 c1 sig2 c2]</var>)</i></dt>
</dl>
<p> For a given domain <var>x</var> and parameters <var>params</var> (or
<var>[sig1 c1 sig2 c2]</var>), return the corresponding <var>y</var> values for the
two-sided Gaussian composite membership function. This membership function is
a smooth curve calculated from two Gaussian membership functions as follows:
</p>
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<p> Given parameters <var>sig1</var>, <var>c1</var>, <var>sig2</var>, and <var>c2</var>, that define
two Gaussian membership functions, let:
</p>
<pre class="verbatim"> f1(x) = exp((-(x - c1)^2)/(2 * sig1^2)) if x <= c1
1 otherwise
f2(x) = 1 if x <= c2
exp((-(x - c2)^2)/(2 * sig2^2)) otherwise
</pre>
<p> Then gauss2mf is given by:
</p>
<pre class="verbatim"> f(x) = f1(x) * f2(x)
</pre>
<p> The argument <var>x</var> must be a real number or a non-empty vector of strictly
increasing real numbers, and <var>sig1</var>, <var>c1</var>, <var>sig2</var>, and <var>c2</var>
must be real numbers.
Gauss2mf always returns a continuously differentiable curve with values in
the range [0, 1].
</p>
<p> If <var>c1</var> < <var>c2</var>, gauss2mf is a normal membership function (has a
maximum value of 1), with the rising curve identical to that of f1(x) and a
falling curve identical to that of f2(x), above. If <var>c1</var> >= <var>c2</var>,
gauss2mf returns a subnormal membership function (has a maximum value less
than 1).
</p>
<p> To run the demonstration code, type "<tt>demo gauss2mf</tt>" (without the quotation
marks) at the Octave prompt.
</p>
<p> <strong>See also: </strong>
<a href="dsigmf.html">dsigmf</a>,
<a href="gaussmf.html">gaussmf</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 = -10:0.2:10;
params = [3 0 1.5 2];
y1 = gauss2mf(x, params);
params = [1.5 0 3 2];
y2 = gauss2mf(x, params);
params = [1.5 2 3 0];
y3 = gauss2mf(x, params);
figure('NumberTitle', 'off', 'Name', 'gauss2mf demo');
plot(x, y1, 'r;params = [3 0 1.5 2];', 'LineWidth', 2);
hold on ;
plot(x, y2, 'b;params = [1.5 0 3 2];', 'LineWidth', 2);
hold on ;
plot(x, y3, 'g;params = [1.5 2 3 0];', 'LineWidth', 2);
ylim([-0.1 1.1]);
xlabel('Crisp Input Value', 'FontWeight', 'bold');
ylabel('Degree of Membership', 'FontWeight', 'bold');
grid;
hold;
</pre></td></tr></tbody>
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