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__END__

=head1 NAME

AI::Fuzzy - Perl extension for Fuzzy Logic

=head1 SYNOPSIS

  use AI::Fuzzy;

  my $f = new AI::Fuzzy::Axis;
  my $l = new AI::Fuzzy::Label("toddler",      1, 1.5, 3.5);

  $f->addlabel("baby",        -1,   1, 2.5);
  $f->addlabel($l);
  $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 => " . $f->labelvalue($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));
  
  my $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__

=head1 DESCRIPTION

AI::Fuzzy really consists of three modules - AI::Fuzzy::Axis, AI::Fuzzy::Label, and
AI::Fuzzy::Set.  

A fuzzy set is simply a mathematical set to which members can
I<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 axis holds fuzzy labels and can be used to classify values
by examining the degree to which they belong to several labels, 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 classifies a particular range of the Axis. In the above example 
the label is one of "cold", "cool", or "warm". A fuzzy label defines how
much a crisp value belongs to the classifier such as "cold", "warm", or "cool". 



=head2 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

=head2 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