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<!DOCTYPE html>
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<title>Octave Fuzzy Logic Toolkit: psigmf</title>
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Membership Functions
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Function Reference: <b><code>psigmf</code></b>
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<dl>
<dt><u>Function File:</u> <var>y</var> = <b>psigmf</b><i> (<var>x</var>, <var>params</var>)</i></dt>
<dt><u>Function File:</u> <var>y</var> = <b>psigmf</b><i> (<var>[x1 x2 ... xn]</var>, <var>[a1 c1 a2 c2]</var>)</i></dt>
</dl>
<p> For a given domain <var>x</var> and parameters <var>params</var> (or
<var>[a1 c1 a2 c2]</var>), return the corresponding <var>y</var> values for the product
of two sigmoidal membership functions.
</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>a1</var>, <var>c1</var>, <var>a2</var>, and <var>c2</var> must
be real numbers. This membership function satisfies the equation:
</p>
<pre class="verbatim"> f(x) = (1/(1 + exp(-a1*(x - c1)))) * (1/(1 + exp(-a2*(x - c2))))
</pre>
<p> The function is bounded above by 1 and below by 0.
</p>
<p> If <var>a1</var> is positive, <var>a2</var> is negative, and <var>c1</var> and <var>c2</var> are
far enough apart with <var>c1</var> < <var>c2</var>, then:
</p>
<pre class="verbatim"> (a1)/4 ~ the rising slope at c1
c1 ~ the left inflection point
(a2)/4 ~ the falling slope at c2
c2 ~ the right inflection point
</pre>
<p> and at each inflection point, the value of the function is about 0.5:
</p>
<pre class="verbatim"> f(c1) ~ f(c2) ~ 0.5.
</pre>
<p> (Here, the symbol ~ means "approximately equal".)
</p>
<p> To run the demonstration code, type "<tt>demo psigmf</tt>" (without the quotation
marks) at the Octave prompt.
</p>
<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="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 = 0:100;
params = [0.5 20 -0.3 60];
y1 = psigmf(x, params);
params = [0.3 20 -0.2 60];
y2 = psigmf(x, params);
params = [0.2 20 -0.1 60];
y3 = psigmf(x, params);
figure('NumberTitle', 'off', 'Name', 'psigmf demo');
plot(x, y1, 'r;params = [0.5 20 -0.3 60];', 'LineWidth', 2)
hold on;
plot(x, y2, 'b;params = [0.3 20 -0.2 60];', 'LineWidth', 2)
hold on;
plot(x, y3, 'g;params = [0.2 20 -0.1 60];', 'LineWidth', 2)
ylim([-0.1 1.1]);
xlabel('Crisp Input Value', 'FontWeight', 'bold');
ylabel('Degree of Membership', 'FontWeight', 'bold');
grid;
</pre></td></tr></tbody>
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