# NAME

AI::Fuzzy - Perl extension for Fuzzy Logic

# SYNOPSIS

``````  use AI::Fuzzy;

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

for (my \$x = 0; \$x<50; \$x+=4) {
print "\$x years old => " . \$f->label(\$x) . "\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=>100, 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;``````

## 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

@l = 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

Michal Wallace (sabren@manifestation.com)