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NAME
    AI::Fuzzy - Perl extension for Fuzzy Logic

SYNOPSIS
      use AI::Fuzzy;

      my $f = new AI::Fuzzy::Label;

      $f->addlabel("baby",        -1,   1, 2.5);
      $f->addlabel("toddler",      1, 1.5, 3.5);
      $f->addlabel("little kid",   2,   7,  12);
      $f->addlabel("kid",          6,  10,  14);
      $f->addlabel("teenager",    12,  16,  20);
      $f->addlabel("young adult", 18,  27,  35);
      $f->addlabel("adult",       25,  50,  75);
      $f->addlabel("senior",      60,  80, 110);
      $f->addlabel("relic",      100, 150, 200);

      for (my $x = 0; $x<50; $x+=4) {
          print "$x years old => " . $f->label($x) . "\n";
      }

      $a = new AI::Fuzzy::Set( x1 => .3, x2 => .5, x3 => .8, x4 => 0, x5 => 1);
      $b = new AI::Fuzzy::Set( x5 => .3, x6 => .5, x7 => .8, x8 => 0, x9 => 1);
      print "a is: " . $a->as_string . "\n"; 
      print "b is: " . $b->as_string . "\n"; 
  
      print "a is equal to b" if ($a->equal($b));
  
      $c = $a->complement();
      print "complement of a is: " . $c->as_string . "\n"; 
  
      $c = $a->union($b);
      print "a union b is: " . $c->as_string . "\n"; 
  
      $c = $a->intersection($b);
      print "a intersection b is: " . $c->as_string . "\n"; 

    __END__

DESCRIPTION
    AI::Fuzzy really consists of two modules - AI::Fuzzy::Label and
    AI::Fuzzy::Set.

    A fuzzy set is simply a mathematical set to which members can
    *partially* belong. For example, a particular shade of gray may
    partially belong to the set of dark colors, whereas black would have
    full membership, and lemon yellow would have almost no membership.

    A fuzzy labeler classifies a particular crisp value by examining the
    degree to which it belongs to several sets, and selecting the most
    appropriate. For example, it can decide whether to call water at 60
    degrees Farenheight "cold", "cool", or "warm". A fuzzy label might be
    one of these labels, or a fuzzy set describing to what degree each of
    the labels describes the particular value in question.

  Fuzzy Sets

    AI::Fuzzy:Set has these methods:

        $fs = B<new> AI::Fuzzy::Set;

        # here, "Bob" is unquestionably tall.. the others less so.
        $fs_tall_people = B<new> AI::Fuzzy::Set( Lester=>.34, Bob=>1.00, Max=>.86 );
   
        # $x will be .86
        $x = B<membership> $fs_tall_people, "Max";

        # get list of members, sorted from least membership to greatest:
        @shortest_first = B<members> $fs_tall_people;

        $fs = B<new> AI::Fuzzy::Set( x1 => .3, x2 => .5, x3 => .8, x4 => 0, x5 => 1);

        B<complement>, B<union>, B<intersection>
        Thesie are the fuzzy set version of the typical functions.
   
        B<equal>
        Returns true if the sets have the same elements and those elements
        are all equal.

       B<as_string>
       Prints the set as tuples:
            $b = new AI::Fuzzy::Set( x5 => .3, x6 => .5, x7 => .8, x8 => 0, x9 => 1);
            print "b is: " . $b->as_string . "\n"; 
        prints:
            b is: x8/0, x5/0.3, x6/0.5, x7/0.8, x9/1

  Fuzzy Labels

    A Fuzzy::Label label has four attributes: the text of the label (it can
    be any scalar, really), and three numbers: low, mid, high if you imagine
    a cartesian plane (remember graph paper in algebra?) of all possible
    values, the label applies to a particular range. the graph might look
    something like this:

              |Y               * (mid, 1)
              |               /  \
              |             /    \
              |           /       \
              |         /          \
             -|-------*-------------*------- X
                       (low,0)      (high,0)
         
    the Y value is applicability of the label for a given X value

    the mid number is the "pure" value. eg, orange is at 0 or 360 degrees on
    the color wheel. the label applies 100% at the mid point.

    the low and high numbers are the two points at which the label ceases to
    apply.

    note that labels can overlap, and that the mid number isn't always in
    the exact center, so the slope of the two sides may vary...

    $fl = new AI::FuzzyLabel;

    $fl->addlabel( "hot", 77, 80, 100 ); # what I consider hot. :) (in
    Farenheit, of course!)

    $a = $fl->applicability($label, $value); # $a is now the degree to which
    $label applies to $value

    $l = $fl->label ($value); # applies a label to $value

    @l = $fl->label($value); # returns a list of labels and their
    applicability values

    $s = new AI::Fuzzy::Set( $fl->label($value) ); # same thing, but now
    it's an object

    @range = $fl->range(); # returns a list of labels, sorted by their
    midpoints # eg: ("cold", "cool", "lukewarm", "warm", "hot")

AUTHOR
    Tom Scanlan <tscanlan@openreach.com>, current maintainer

    Michal Wallace (sabren@manifestation.com), original author

SEE ALSO
    Move along, nothing to "see also" here...

BUGS
    Please send any bugs to Tom Scanlan <tscanlan@openreach.com>