# NAME

AI::Fuzzy - Perl extension for Fuzzy Logic

# 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__

# 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 *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".

## 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::Fuzzy::Label ( "hot", 77, 80, 100 ); $fx = new AI::Fuzzy::Label ( "cold", 0, 10, 200 ); # what I consider hot. :) (in Farenheit, of course!)

if ( $fl->lessthan($fx) ) { print "the laws of nature have changed\n"; }

# there is a lessthan, greaterthan, lessequal, greaterequal, and between # that functions as above or using <,>,<=,>=

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

## Fuzzy Axis

A Fuzzy::Axis maintains a hash of labels. Thus you can now look at how values apply to the full range of labels. The graph of an Axis might look like this:

```
|Y * (mid, 1)
| /\/ \ /|
| /- -\ / /\ \ / |
| / \-/ / \ \ / | (some function on some range of x)
| | / \ /\ ---*-|
-|---------*-----------*------- X
(low,0) (high,0)
```

the Y value is still the applicability of the label for a given X value, but there are three labels on this Axis. A different X value may put your value into a new label.

$fl = new AI::Fuzzy::Axis;

$fl->addlabel($label); # add a label created as in AI::Fuzzy::Label docs

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

$l = $fl->label ("labelname"); # returns the label object named "labelname"

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

@l = $fl->labelvalue($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") =head1 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>