Ala Qumsieh

NAME

AI::FuzzyInference - A module to implement a Fuzzy Inference System.

SYNOPSYS

    use AI::FuzzyInference;

    my $s = new AI::FuzzyInference;

    $s->inVar('service', 0, 10,
          poor      => [0, 0,
                        2, 1,
                        4, 0],
          good      => [2, 0,
                        4, 1,
                        6, 0],
          excellent => [4, 0,
                        6, 1,
                        8, 0],
          amazing   => [6, 0,
                        8, 1,
                        10, 0],
          );

    $s->inVar('food', 0, 10,
          poor      => [0, 0,
                        2, 1,
                        4, 0],
          good      => [2, 0,
                        4, 1,
                        6, 0],
          excellent => [4, 0,
                        6, 1,
                        8, 0],
          amazing   => [6, 0,
                        8, 1,
                        10, 0],
          );

    $s->outVar('tip', 5, 30,
           poor      => [5, 0,
                         10, 1,
                         15, 0],
           good      => [10, 0,
                         15, 1,
                         20, 0],
           excellent => [15, 0,
                         20, 1,
                         25, 0],
           amazing   => [20, 0,
                         25, 1,
                         30, 0],
           );

    $s->addRule(
            'service=poor      & food=poor'      => 'tip=poor',
            'service=good      & food=poor'      => 'tip=poor',
            'service=excellent & food=poor'      => 'tip=good',
            'service=amazing   & food=poor'      => 'tip=good',

            'service=poor      & food=good'      => 'tip=poor',
            'service=good      & food=good'      => 'tip=good',
            'service=excellent & food=good'      => 'tip=good',
            'service=amazing   & food=good'      => 'tip=excellent',

            'service=poor      & food=excellent' => 'tip=good',
            'service=good      & food=excellent' => 'tip=excellent',
            'service=excellent & food=excellent' => 'tip=excellent',
            'service=amazing   & food=excellent' => 'tip=amazing',

            'service=poor      & food=amazing'   => 'tip=good',
            'service=good      & food=amazing'   => 'tip=excellent',
            'service=excellent & food=amazing'   => 'tip=amazing',
            'service=amazing   & food=amazing'   => 'tip=amazing',

            );

    $s->compute(service => 2,
            food    => 7);

DESCRIPTION

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: fuzzification, inference, aggregation and defuzzification.

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.

Inference

In this step, all the defined rules are examined. Each rule has two parts: the precedent and the consequent. The degree of support for each rule is computed by applying fuzzy operators (and, 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 (implicate) the consequent part of the rule, generating modified fuzzy sets.

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.

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 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.

PUBLIC METHODS

The module has the following public methods:

new()

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

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 & for logical AND, | for logical OR, or ! for logical NOT. The second argument is used to set what method to use for the given operator. The following values are possible:

&
min

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

product

The result of A and B is A * B.

|
max

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

sum

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

!
complement

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

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

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:

clip

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

scale

This scales the output fuzzy set by multiplying it by its support value.

aggregation()

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

max

The fuzzy sets are combined by taking at each point the maximum value of all the fuzzy sets at that point. This is the default.

defuzzification()

This method is used to set/query the defuzzification method used to extract a single crisp value from the aggregated fuzzy set. It takes one optional argument which specifies the name of the defuzzification method used. This can be one of the following:

centroid

The centroid (aka center of mass and center of gravity) of the aggregated fuzzy set is computed and returned. This is the default.

inVar()

This method defines an input variable, along with its universe of discourse, and its term sets. Here's an example:

      $obj->inVar('height',
                  5, 8,   # xmin, xmax (in feet, say)
                  'tall' => [5,   0,
                             5.5, 1,
                             6,   0],
                  'medium' => [5.5, 0,
                             6.5, 1,
                             7, 0],
                  'short' => [6.5, 0,
                             7, 1]
                  );

This example defines an input variable called height. The minimum possible value for height is 5, and the maximum is 8. It also defines 3 term sets associated with height: tall, medium and short. The shape of each of these triangular term sets is completely specified by the supplied anonymous array of indices.

outVar()

This method defines an output variable, along with its universe of discourse, and its term sets. The arguments are identical to those for the inVar() method.

addRule()

This method is used to add the fuzzy rules. Its arguments are hash-value pairs; the keys are the precedents and the values are the consequents. Each antecedent has to be a combination of 1 or more strings. The strings have to be separated by & or | indicating the fuzzy AND and OR operations respectively. Each consequent must be a single string. Each string has the form: var = term_set. Spaces are completely optional. Example:

    $obj->addRule('height=short & weight=big' => 'diet = necessary',
                  'height=tall & weight=tiny' => 'diet = are_you_kidding_me');

The first rule basically says If the height is short, and the weight is big, then diet is necessary.

compute()

This method takes as input a set of hash-value pairs; the keys are names of input variables, and the values are the values of the variables. It runs those values through the FIS, generating corresponding values for the output variables. It always returns a true value. To get the actual values of the output variables, look at the value() method below. Example:

    $obj->compute(x => 5,
                  y => 24);

Note that any subsequent call to compute() will implicitly clear out the old computed values before recomputing the new ones. This is done through a call to the reset() method below.

value()

This method returns the value of the supplied output variable. It only works for output variables (defined using the outVar() method), and only returns useful results after a call to compute() has been made.

reset()

This method resets all the data structures used to compute crisp values of the output variables. It is implicitly called by the compute() method above.

INSTALLATION

It's all in pure Perl. Just place it somewhere and point your @INC to it.

But, if you insist, here's the traditional way:

To install this module type the following:

   perl Makefile.PL
   make
   make test
   make install

AUTHOR

Copyright 2002, Ala Qumsieh. All rights reserved. This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself.

Address bug reports and comments to: aqumsieh@cpan.org




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