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<HTML>  <HEAD>    <!--SCRIPT LANGUAGE="JavaScript" SRC="http://a1835.g.akamai.net/f/1835/276/3h/www.netlibrary.com/include/js/dictionary_library.js"></SCRIPT>    <SCRIPT LANGUAGE="JavaScript">      if (!opener){document.onkeyup=parent.turnBookPage;}    </SCRIPT!-->    <META HTTP-EQUIV="Cache-Control" CONTENT="no-cache">    <META HTTP-EQUIV="Pragma" CONTENT="no-cache">    <META HTTP-EQUIV="Expires" CONTENT="-1"><META http-equiv="Content-Type" content="text/html; charset=windows-1252"><SCRIPT>var PrevPage="Page_115";var NextPage="Page_117";var CurPage="Page_116";var PageOrder="127";</SCRIPT>  <TITLE>Document</TITLE>  </HEAD>  <BODY BGCOLOR="#FFFFFF"><CENTER><TABLE BORDER=0 WIDTH=100% CELLPADDING=0><TR><TD ALIGN=CENTER>  <TABLE BORDER=0 CELLPADDING=2 CELLSPACING=0 WIDTH=100%>  <TR>  <TD ALIGN=LEFT><A HREF='Page_115.html'>Previous</A></TD>  <TD ALIGN=RIGHT><A HREF='Page_117.html'>Next</A></TD>  </TR>  </TABLE></TD></TR><TR><TD ALIGN=LEFT><P><A NAME='JUMPDEST_Page_116'/><A NAME='{3F4}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH='100%'><TR><TD ALIGN=RIGHT><FONT FACE='Times New Roman, Times, Serif' SIZE=2 COLOR=#FF0000>Page 116</FONT></TD></TR></TABLE><A NAME='{3F5}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5 WIDTH=24><IMG SRC='tab.gif' BORDER=0 WIDTH=24 HEIGHT=1></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5 WIDTH=24><IMG SRC='tab.gif' BORDER=0 WIDTH=24 HEIGHT=1></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=2><I>As the complexity of a system increases, our ability to make precise and yet significant statements about its behavior diminishes until a threshold is reached beyond which precision and significance (or relevance) become almost mutually exclusive characteristics.</I></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{3F6}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=3>Much of this complexity, he realized, came from the way in which the variables of the system were represented and manipulated. Since these variables could only represent the state of a phenomenon as either on or off, the math necessary to evaluate operations at various &quot;border&quot; states became increasingly complex, which at some point became a morass of equations providing little insight about the underlying process. Zadeh called this state the <I>principle of incompatibility.</I></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{3F7}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=3>Fuzzy logic is a calculus of compatibility. In fuzzy logic there is no black or white, there is instead a degree of gray in both. Everything is measured in <I>degrees of membership.</I> Fuzziness, the measure of how well an instance (value) conforms to a semantic ideal or concept, describes the degree of membership in a fuzzy set. This degree of membership can be viewed as the level of compatibility between an instance from the set's domain and the concept overlying the set. For example, in the fuzzy set WILL BUY, the value YES has a degree [.31] meaning that it is only moderately compatible with WILL BUY. This is called a &quot;measure of fuzziness&quot; because it is used to assess the degree of ambiguity or uncertainty attached to each fuzzy set. It is important to realize that a website visitor can be a member of different fuzzy sets simultaneously:</FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{3F8}'/><TABLE CELLPADDING=0 CELLSPACING=0 BORDER=0 WIDTH='100%'><TR><TD HEIGHT=12></TD></TR><TR><TD><TABLE CELLSPACING=0 BORDER=0 BORDERCOLOR=#000000 RULES=ALL WIDTH=616 CELLPADDING=5><TR><TD WIDTH=616 VALIGN=TOP><FONT FACE='Times New Roman, Times, Serif' SIZE=2>IF WILL BUY THEN [.31]</FONT></TD></TR><TR><TD WIDTH=616 VALIGN=TOP><FONT FACE='Times New Roman, Times, Serif' SIZE=2>IF WANTS INFO THEN [.35]</FONT></TD></TR><TR><TD WIDTH=616 VALIGN=TOP><FONT FACE='Times New Roman, Times, Serif' SIZE=2>IF WILL NOT BUY THEN [.34].</FONT></TD></TR></TABLE></TD></TR></TABLE><BR><A NAME='{3F9}'/><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0><TR>  <TD ROWSPAN=5></TD>  <TD COLSPAN=3 HEIGHT=12></TD>  <TD ROWSPAN=5></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR><TD></TD>  <TD><FONT FACE='Times New Roman, Times, Serif' SIZE=3>More and more, fuzzy logic is being used with neural networks, much like genetic algorithms. However, it is not being used at the front end of neural networks, to optimize their setting, but instead to explain their &quot;black-box&quot; findings. The key benefit of fuzzy logic is that it allows for imprecise states to be categorized with simple &quot;IF/THEN&quot; relations, which are easy to verify and optimize. Conversely, a key benefit of neural networks is that they learn from data sets; thus a combination of both technologies provides the best of both worlds. One data mining vendor who already incorporates this type of fuzzy logic and neural network mixture is Data Engine from Management Intelligenter Technologien GmbH. For the Web data miner, fuzzy logic offers a powerful technology for data com-</FONT><FONT FACE='Times New Roman, Times, Serif' SIZE=3 COLOR=#FFFF00><!-- soft --></FONT></TD><TD></TD></TR><TR>  <TD COLSPAN=3></TD></TR><TR>  <TD COLSPAN=3 HEIGHT=1></TD></TR></TABLE><A NAME='{3FA}'/></FORM></P></TD></TR></TABLE><P><FONT SIZE=0 COLOR=WHITE></CENTER><A NAME="bottom">&nbsp;</A><!-- netLibrary.com Copyright Notice -->  </BODY></HTML>

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