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    # Left 
    my $x0 = shift @x;
    my $y0 = shift @y;

    my (@areas, $x1, $y1);

    AREA:
    while (@x) {
        # Right egde of area
        $x1 = shift @x;
        $y1 = shift @y;

        # Each area is build of a rectangle and a top placed triangle
        # Each of them might have a height of zero

        # Area and local centroid of base rectangle
        my $a1 = abs(($x1 - $x0) * ($y0 < $y1 ? $y0 : $y1));
   	my $c1 = $x0 + 0.5 * ($x1 - $x0);

        # Area and local centroid of triangle on top of rectangle
        my $a2 = abs(0.5 * ($x1 - $x0) * ($y1 - $y0));
        my $c2 = (1/3) * ($x0 + $x1 + ($y1 > $y0 ? $x1 : $x0));

        # Total area of block
        my $ta = $a1 + $a2;
   	next AREA if $ta == 0;

        # Total centroid of block
        my $c = ( $c1*$a1 + $c2*$a2 ) / $ta;

        # Store them for final calculation of average
        push @areas, [$c, $ta];
    }
    continue {
        # Left edge of next area
        ($x0, $y0) = ($x1, $y1);
    };

    # Sum of area
    my $ta = 0;
    $ta += $_->[1] for @areas;

    croak "Function has no height --> no centroid" unless $ta;

    # Final Centroid in x direction
    my $c = 0;
    $c += $_->[0] * $_->[1] for @areas;
    return $c / $ta;
}

sub fuzzify {
    my ($self, $val) = @_;

    my $fun = $self->memb_fun;
    croak "No valid membership function"
        unless @{$fun->[0]}; # at least one x

    return $self->{degree} = $self->_interpol( $fun => $val );
}

sub reset {
    my ($self) = @_;
    $self->{degree} = 0;
    $self;
}

# Replace a membership function
# To be called by variable->change_set( 'setname' => $new_fun );
sub replace_memb_fun {
    my ($self, $new_fun) = @_;
    $self->{memb_fun} = $new_fun;
    return;
}

1;

=pod

=head1 NAME

AI::FuzzyEngine::Set - Class used by AI::FuzzyEngine. 

=head1 DESCRIPTION

Please see L<AI::FuzzyEngine> for a description. 

=head1 SUPPORT

You can find documentation for this module with the perldoc command.

    perldoc AI::FuzzyEngine

=head1 AUTHOR

Juergen Mueck, jmueck@cpan.org

=head1 COPYRIGHT

Copyright (c) Juergen Mueck 2013.  All rights reserved.

This library is free software; you can redistribute it and/or
modify it under the same terms as Perl itself.

=cut