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<!DOCTYPE html>
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<title>Octave Fuzzy Logic Toolkit: sigmf</title>
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Octave Fuzzy Logic Toolkit
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Membership Functions
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Function Reference: <b><code>sigmf</code></b>
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<dl>
<dt><u>Function File:</u> <var>y</var> = <b>sigmf</b><i> (<var>x</var>, <var>params</var>)</i></dt>
<dt><u>Function File:</u> <var>y</var> = <b>sigmf</b><i> (<var>[x1 x2 ... xn]</var>, <var>[a c]</var>)</i></dt>
</dl>
<p> For a given domain <var>x</var> and parameters <var>params</var> (or <var>[a c]</var>),
return the corresponding <var>y</var> values for the sigmoidal membership
function.
</p>
<div class="ms-5">
<p> The argument <var>x</var> must be a real number or a non-empty vector of strictly
increasing real numbers, and <var>a</var> and <var>c</var> must be real numbers. This
membership function satisfies the equation:
</p>
<pre class="verbatim"> f(x) = 1/(1 + exp(-a*(x - c)))
</pre>
<p> which always returns values in the range [0, 1].
</p>
<p> The parameters a and c specify:
</p>
<pre class="verbatim"> a == the slope at c
c == the inflection point
</pre>
<p> and at the inflection point, the value of the function is 0.5:
</p>
<pre class="verbatim"> f(c) == 0.5.
</pre>
<p> To run the demonstration code, type "<tt>demo sigmf</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="gaussmf.html">gaussmf</a>,
<a href="gbellmf.html">gbellmf</a>,
<a href="pimf.html">pimf</a>,
<a href="psigmf.html">psigmf</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 = 0:100;
params = [0.3 40];
y1 = sigmf(x, params);
params = [0.2 40];
y2 = sigmf(x, params);
params = [0.1 40];
y3 = sigmf(x, params);
figure('NumberTitle', 'off', 'Name', 'sigmf demo');
plot(x, y1, 'r;params = [0.3 40];', 'LineWidth', 2)
hold on;
plot(x, y2, 'b;params = [0.2 40];', 'LineWidth', 2)
hold on;
plot(x, y3, 'g;params = [0.1 40];', 'LineWidth', 2)
ylim([-0.1 1.2]);
xlabel('Crisp Input Value', 'FontWeight', 'bold');
ylabel('Degree of Membership', 'FontWeight', 'bold');
grid;
</pre></td></tr></tbody>
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