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<b>let </b><font color="Maroon" title="c1">C</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font>, <font color="Maroon" title="c4">h</font> be    <a href="fuzzy_1.html#M1" title="FUZZY_1:mode.1">Membership_Func</a> of <font color="Maroon" title="c1">C</font>;<br/>







<font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c4">h</font></span>)</span> = 
 <a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c2">f</font>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <span class="p3">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c4">h</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_1.html#T12" title="FUZZY_1:th.12">FUZZY_1:12</a></i>
<br/>.= 
 <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c2">f</font>,<span class="p2">(<span class="default"><a href="fuzzy_1.html#K3" title="FUZZY_1:func.3">1_minus</a> <font color="Maroon" title="c3">g</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">h</font></span>)</span>
<b>by </b><i><a class="ref" href="fuzzy_1.html#T10" title="FUZZY_1:th.10">FUZZY_1:10</a></i>
;<br/>
<b>hence </b><a NAME="E2:12"/>
<font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c4">h</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="fuzzy_1.html#K2" title="FUZZY_1:func.2">max</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f</font> <a href="fuzzy_2.html#K1" title="FUZZY_2:func.1">\</a> <font color="Maroon" title="c3">g</font></span>)</span>,<span class="p1">(<span class="default"><a href="fuzzy_1.html#K1" title="FUZZY_1:func.1">min</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">h</font></span>)</span>
 ;<br/>


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