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TNormFunction Enumeration Reference
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<h1>TNormFunction</h1>
<div class="declaration">
<div class="language">
<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">enum</span> <span class="kt">TNormFunction</span></code></pre>
</div>
</div>
<p>Describes a T-norm function, usually used for forming an intersection of fuzzy sets.</p>
<p>A function <code>T</code> must satisfy the following axioms in order to be T-normed:</p>
<ol>
<li>Boundary condition: <code>T(1, 1) = 1</code>, <code>T(1, 0) = 0</code>, <code>T(0, 1) = 0</code>, <code>T(0, 0) = 0</code></li>
<li>Commutativity: <code>T(a, b) = T(b, a)</code></li>
<li>Monotonic: <code>If a &lt;= a&#39; and b &lt;= b&#39; Then T(a, b) &lt;= T(a&#39;, b&#39;)</code></li>
<li>Associativity: <code>T(T(a, b), c) = T(a, T(b, c))</code></li>
</ol>
</section>
<section class="section task-group-section">
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<ul>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO7minimumyA2CmF"></a>
<a name="//apple_ref/swift/Element/minimum" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO7minimumyA2CmF">minimum</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="n">minimum</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO11lukasiewiczyA2CmF"></a>
<a name="//apple_ref/swift/Element/lukasiewicz" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO11lukasiewiczyA2CmF">lukasiewicz</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="n">lukasiewicz</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO7productyA2CmF"></a>
<a name="//apple_ref/swift/Element/product" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO7productyA2CmF">product</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="n">product</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO4weakyA2CmF"></a>
<a name="//apple_ref/swift/Element/weak" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO4weakyA2CmF">weak</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="k">weak</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO8hamacheryACSd_tcACmF"></a>
<a name="//apple_ref/swift/Element/hamacher(gamma:)" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO8hamacheryACSd_tcACmF">hamacher(gamma:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="nf">hamacher</span><span class="p">(</span><span class="nv">gamma</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO14duboisAndPradeyACSd_tcACmF"></a>
<a name="//apple_ref/swift/Element/duboisAndPrade(alpha:)" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO14duboisAndPradeyACSd_tcACmF">duboisAndPrade(alpha:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="nf">duboisAndPrade</span><span class="p">(</span><span class="nv">alpha</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO5yageryACSd_tcACmF"></a>
<a name="//apple_ref/swift/Element/yager(p:)" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO5yageryACSd_tcACmF">yager(p:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="nf">yager</span><span class="p">(</span><span class="nv">p</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO5frankyACSd_tcACmF"></a>
<a name="//apple_ref/swift/Element/frank(lambda:)" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO5frankyACSd_tcACmF">frank(lambda:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="nf">frank</span><span class="p">(</span><span class="nv">lambda</span><span class="p">:</span> <span class="kt">Double</span><span class="p">)</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO6customyACS2d_SdtccACmF"></a>
<a name="//apple_ref/swift/Element/custom(_:)" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO6customyACS2d_SdtccACmF">custom(_:<wbr>)</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="k">case</span> <span class="nf">custom</span><span class="p">((</span><span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">,</span> <span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">)</span></code></pre>
</div>
</div>
</section>
</div>
</li>
<li class="item">
<div>
<code>
<a name="/s:9FuzzySets13TNormFunctionO8functionyS2d_Sdtcvp"></a>
<a name="//apple_ref/swift/Property/function" class="dashAnchor"></a>
<a class="token" href="#/s:9FuzzySets13TNormFunctionO8functionyS2d_Sdtcvp">function</a>
</code>
</div>
<div class="height-container">
<div class="pointer-container"></div>
<section class="section">
<div class="pointer"></div>
<div class="abstract">
<p>Undocumented</p>
</div>
<div class="declaration">
<h4>Declaration</h4>
<div class="language">
<p class="aside-title">Swift</p>
<pre class="highlight swift"><code><span class="kd">public</span> <span class="k">var</span> <span class="nv">function</span><span class="p">:</span> <span class="p">(</span><span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">,</span> <span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">)</span> <span class="o">-&gt;</span> <span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span> <span class="p">{</span> <span class="k">get</span> <span class="p">}</span></code></pre>
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