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FuzzyInference.pm  view on Meta::CPAN

This module implements a fuzzy inference system. Very briefly, an FIS
is a system defined by a set of input and output variables, and a set
of fuzzy rules relating the input variables to the output variables.
Given crisp values for the input variables, the FIS uses the fuzzy rules
to compute a crisp value for each of the output variables.

The operation of an FIS is split into 4 distinct parts: I<fuzzification>,
I<inference>, I<aggregation> and I<defuzzification>.

=head2 Fuzzification

In this step, the crisp values of the input variables are used to
compute a degree of membership of each of the input variables in each
of its term sets. This produces a set of fuzzy sets.

=head2 Inference

In this step, all the defined rules are examined. Each rule has two parts:
the I<precedent> and the I<consequent>. The degree of support for each
rule is computed by applying fuzzy operators (I<and>, I<or>) to combine
all parts of its precendent, and generate a single crisp value. This value
indicates the "strength of firing" of the rule, and is used to reshape
(I<implicate>) the consequent part of the rule, generating modified
fuzzy sets.

=head2 Aggregation

Here, all implicated fuzzy sets of the fired rules are combined using
fuzzy operators to generate a single fuzzy set for each of the
output variables.

=head2 Defuzzification

Finally, a defuzzification operator is applied to the aggregated fuzzy
set to generate a single crisp value for each of the output variables.

For a more detailed explanation of fuzzy inference, you can check out
the tutorial by Jerry Mendel at
S<http://sipi.usc.edu/~mendel/publications/FLS_Engr_Tutorial_Errata.pdf>.

Note: The terminology used in this module might differ from that used
in the above tutorial.

=head1 PUBLIC METHODS

The module has the following public methods:

=over 4

=item new()

This is the constructor. It takes no arguments, and returns an
initialized AI::FuzzyInference object.

=item operation()

This method is used to set/query the fuzzy operations. It takes at least
one argument, and at most 2. The first argument specifies the logic
operation in question, and can be either C<&> for logical I<AND>,
C<|> for logical I<OR>, or C<!> for logical I<NOT>. The second
argument is used to set what method to use for the given operator.
The following values are possible:

=item &

=over 8

=item min

The result of C<A and B> is C<min(A, B)>. This is the default.

=item product

The result of C<A and B> is C<A * B>.

=back

=item |

=over 8

=item max

The result of C<A or B> is C<max(A, B)>. This is the default.

=item sum

The result of C<A or B> is C<min(A + B, 1)>.

=back

=item !

=over 8

=item complement

The result of C<not A> is C<1 - A>. This is the default.

=back

The method returns the name of the method to be used for the given
operation.

=item implication()

This method is used to set/query the implication method used to alter
the shape of the implicated output fuzzy sets. It takes one optional
argument which specifies the name of the implication method used.
This can be one of the following:

=over 8

=item clip

This causes the output fuzzy set to be clipped at its support value.
This is the default.

=item scale