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<title>Octave Fuzzy Logic Toolkit: pimf</title>
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Membership Functions
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Function Reference: <b><code>pimf</code></b>
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<dl>
<dt><u>Function File:</u> <var>y</var> = <b>pimf</b><i> (<var>x</var>, <var>params</var>)</i></dt>
<dt><u>Function File:</u> <var>y</var> = <b>pimf</b><i> (<var>[x1 x2 ... xn]</var>, <var>[a b c d]</var>)</i></dt>
</dl>
<p> For a given domain <var>x</var> and parameters <var>params</var> (or <var>[a b c d]</var>),
return the corresponding <var>y</var> values for the pi-shaped membership
function.
</p>
<div class="ms-5">
<p> The argument <var>x</var> must be a real number or a non-empty vector of real
numbers, and <var>a</var>, <var>b</var>, <var>c</var>, and <var>d</var> must be real numbers,
with <var>a</var> < <var>b</var> <= <var>c</var> < <var>d</var>. This membership function
satisfies:
</p>
<pre class="verbatim"> 0 if x <= a
2 * ((x - a)/(b - a))^2 if a < x <= (a + b)/2
1 - 2 * ((x - b)/(b - a))^2 if (a + b)/2 < x < b
f(x) = 1 if b <= x <= c
1 - 2 * ((x - c)/(d - c))^2 if c < x <= (c + d)/2
2 * ((x - d)/(d - c))^2 if (c + d)/2 < x < d
0 if x >= d
</pre>
<p> which always returns values in the range [0, 1].
</p>
<p> To run the demonstration code, type "<tt>demo pimf</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="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 = 0:255;
params = [70 80 100 140];
y1 = pimf(x, params);
params = [50 75 105 175];
y2 = pimf(x, params);
params = [30 70 110 200];
y3 = pimf(x, params);
figure('NumberTitle', 'off', 'Name', 'pimf demo');
plot(x, y1, 'r;params = [70 80 100 140];', 'LineWidth', 2)
hold on;
plot(x, y2, 'b;params = [50 75 105 175];', 'LineWidth', 2)
hold on;
plot(x, y3, 'g;params = [30 70 110 200];', '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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