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453 lines
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SNormFunction Enumeration Reference
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<a href="../Structs/IterableFuzzySet/Element.html">– Element</a>
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<a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a>
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<article class="main-content">
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<section>
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<section class="section">
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<h1>SNormFunction</h1>
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<div class="declaration">
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<div class="language">
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<pre class="highlight swift"><code><span class="kd">public</span> <span class="kd">enum</span> <span class="kt">SNormFunction</span></code></pre>
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</div>
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</div>
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<p>Describes a S-norm (T-conorm) function, usually used for forming a union of fuzzy sets.</p>
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<p>A function <code>S</code> must satisfy the following axioms in order to be S-normed (T-conormed):</p>
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<ol>
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<li>Boundary condition: <code>S(1, 1) = 1</code>, <code>S(1, 0) = 1</code>, <code>S(0, 1) = 1</code>, <code>S(0, 0) = 0</code></li>
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<li>Commutativity: <code>S(a, b) = S(b, a)</code></li>
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<li>Monotonic: <code>If a <= a' and b <= b' Then S(a, b) <= S(a', b')</code></li>
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<li>Associativity: <code>S(T(a, b), c) = S(a, T(b, c))</code></li>
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</ol>
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</section>
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<section class="section task-group-section">
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<div class="task-group">
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<ul>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO7maximumyA2CmF"></a>
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<a name="//apple_ref/swift/Element/maximum" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO7maximumyA2CmF">maximum</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<pre class="highlight swift"><code><span class="k">case</span> <span class="n">maximum</span></code></pre>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO11lukasiewiczyA2CmF"></a>
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<a name="//apple_ref/swift/Element/lukasiewicz" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO11lukasiewiczyA2CmF">lukasiewicz</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<pre class="highlight swift"><code><span class="k">case</span> <span class="n">lukasiewicz</span></code></pre>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO13probabilisticyA2CmF"></a>
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<a name="//apple_ref/swift/Element/probabilistic" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO13probabilisticyA2CmF">probabilistic</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<pre class="highlight swift"><code><span class="k">case</span> <span class="n">probabilistic</span></code></pre>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO6strongyA2CmF"></a>
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<a name="//apple_ref/swift/Element/strong" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO6strongyA2CmF">strong</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<pre class="highlight swift"><code><span class="k">case</span> <span class="n">strong</span></code></pre>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO8hamacheryACSd_tcACmF"></a>
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<a name="//apple_ref/swift/Element/hamacher(gamma:)" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO8hamacheryACSd_tcACmF">hamacher(gamma:<wbr>)</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<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>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO5yageryACSd_tcACmF"></a>
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<a name="//apple_ref/swift/Element/yager(p:)" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO5yageryACSd_tcACmF">yager(p:<wbr>)</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<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>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO6customyACS2d_SdtccACmF"></a>
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<a name="//apple_ref/swift/Element/custom(_:)" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO6customyACS2d_SdtccACmF">custom(_:<wbr>)</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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<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">-></span> <span class="kt"><a href="../Typealiases.html#/s:9FuzzySets5Gradea">Grade</a></span><span class="p">)</span></code></pre>
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</div>
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</div>
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</section>
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</div>
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</li>
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<li class="item">
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<div>
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<code>
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<a name="/s:9FuzzySets13SNormFunctionO8functionyS2d_Sdtcvp"></a>
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<a name="//apple_ref/swift/Property/function" class="dashAnchor"></a>
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<a class="token" href="#/s:9FuzzySets13SNormFunctionO8functionyS2d_Sdtcvp">function</a>
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</code>
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</div>
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<div class="height-container">
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<div class="pointer-container"></div>
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<section class="section">
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<div class="pointer"></div>
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<div class="abstract">
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<p>Undocumented</p>
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</div>
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<div class="declaration">
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<h4>Declaration</h4>
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<div class="language">
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<p class="aside-title">Swift</p>
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||
<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">-></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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</section>
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<section id="footer">
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<p>© 2022 <a class="link" href="" target="_blank" rel="external noopener">Alexander Ignatov</a>. All rights reserved. (Last updated: 2022-02-08)</p>
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