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    # Implicit application of 'and'
    # Multiple calls to a membership function
    # are similar to 'or' operations:
    $saturation->low( $flow->small(), $cap->avg()  );
    $saturation->low( $flow->small(), $cap->high() );
    $saturation->low( $flow->med(),   $cap->high() );

    # Explicite 'or', 'and' or 'not' possible:
    $saturation->crit( $fe->or( $fe->and( $flow->med(),  $cap->avg()  ),
                                $fe->and( $flow->huge(), $cap->high() ),
                       ),
                 );
    $saturation->over( $fe->not( $flow->small() ),
                       $fe->not( $flow->med()   ),
                       $flow->huge(),
                       $cap->high(),
                 );
    $saturation->over( $flow->huge(), $fe->not( $cap->high() ) );

    # b) deduce output variable(s) (here: from internal variable $saturation)
    $green->decrease( $saturation->low()  );
    $green->ok(       $saturation->crit() );
    $green->increase( $saturation->over() );

    # All sets provide their respective membership degrees: 
    my $saturation_is_over = $saturation->over(); # This is no defuzzification!
    my $green_is_ok        = $green->ok();

    # Defuzzification ( is a matter of the fuzzy variable )
    my $delta_green = $green->defuzzify(); # -5 ... 5

=head2 Using PDL and its threading capability

    use PDL;
    use AI::FuzzyEngine;

    # (Probably a stupide example)
    my $fe        = AI::FuzzyEngine->new();

    # Declare variables as usual
    my $severity  = $fe->new_variable( 0 => 10,
                          low  => [0, 1, 3, 1, 5, 0       ],
                          high => [      3, 0, 5, 1, 10, 1],
                        );

    my $threshold = $fe->new_variable( 0 => 1,
                           low  => [0, 1, 0.2, 1, 0.8, 0,     ],
                           high => [      0.2, 0, 0.8, 1, 1, 1],
                         );
    
    my $problem   = $fe->new_variable( -0.5 => 2,
                           no  => [-0.5, 0, 0, 1, 0.5, 0, 1, 0],
                           yes => [         0, 0, 0.5, 1, 1, 1, 1.5, 1, 2, 0],
                         );

    # Input data is a pdl of arbitrary dimension
    my $data = pdl( [0, 4, 6, 10] );
    $severity->fuzzify( $data );

    # Membership degrees are piddles now:
    print 'Severity is high: ', $severity->high, "\n";
    # [0 0.5 1 1]

    # Other variables might be piddles of other dimensions,
    # but all variables must be expandible to a common 'wrapping' piddle
    # ( in this case a 4x2 matrix with 4 colums and 2 rows)
    my $level = pdl( [0.6],
                     [0.2],
                   );
    $threshold->fuzzify( $level );

    print 'Threshold is low: ', $threshold->low(), "\n";
    # [
    #  [0.33333333]
    #  [         1]
    # ]

    # Apply some rules
    $problem->yes( $severity->high,  $threshold->low );
    $problem->no( $fe->not( $problem->yes )  );

    # Fuzzy results are represented by the membership degrees of sets 
    print 'Problem yes: ', $problem->yes,  "\n";
    # [
    #  [         0 0.33333333 0.33333333 0.33333333]
    #  [         0        0.5          1          1]
    # ]

    # Defuzzify the output variables
    # Caveat: This includes some non-threadable operations up to now
    my $problem_ratings = $problem->defuzzify();
    print 'Problems rated: ', $problem_ratings;
    # [
    #  [         0 0.60952381 0.60952381 0.60952381]
    #  [         0       0.75          1          1]
    # ]

=head1 EXPORT

Nothing is exported or exportable.

=head1 DESCRIPTION

This module is yet another implementation of a fuzzy inference system.
The aim was to  be able to code rules (no string parsing),
but avoid operator overloading,
and make it possible to split calculation into multiple steps.
All intermediate results (memberships of sets of variables)
should be available.

Beginning with v0.2.0 it is PDL aware,
meaning that it can handle piddles (PDL objects)
when running the fuzzy operations.
More information on PDL can be found at L<http://pdl.perl.org/>. 

Credits to Ala Qumsieh and his L<AI::FuzzyInference>,
that showed me that fuzzy is no magic.
I learned a lot by analyzing his code,
and he provides good information and links to learn more about Fuzzy Logics.

=head2 Fuzzy stuff

The L<AI::FuzzyEngine> object defines and provides
the elementary operations for fuzzy sets.
All membership degrees of sets are values from 0 to 1.
Up to now there is no choice with regard to how to operate on sets:

=over 2

=item C<< $fe->or( ... ) >> (Disjunction)

is I<Maximum> of membership degrees

=item C<< $fe->and( ... ) >> (Conjunction)

is I<Minimum> of membership degrees

=item C<< $fe->not( $var->$set ) >> (Negation)

is I<1-degree> of membership degree

=item Aggregation of rules (Disjunction)

is I<Maximum>

=item True C<< $fe->true() >> and false C<< $fe->false() >>

are provided for convenience.

=back

Defuzzification is based on