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Jürgen Mück > AI-FuzzyEngine-v0.1.0 > AI::FuzzyEngine
Module Version: v0.1.0   Source   Latest Release: AI-FuzzyEngine-v0.2.2

# NAME

AI::FuzzyEngine - A small Fuzzy Engine

# SYNOPSIS

```    use AI::FuzzyEngine;

# Engine (or factory) provides fuzzy logical arithmetic
my \$fe = AI::FuzzyEngine->new();

# Disjunction:
my \$a = \$fe->or ( 0.2, 0.5, 0.8, 0.7 ); # 0.8
# Conjunction:
my \$b = \$fe->and( 0.2, 0.5, 0.8, 0.7 ); # 0.2
# Negation:
my \$c = \$fe->not( 0.4 );                # 0.6

# These functions are constitutive for the operations
# on the fuzzy sets of the fuzzy variables:

# VARIABLES (AI::FuzzyEngine::Variable)

# input variables need definition of membership functions of their sets
my \$flow = \$fe->new_variable( 0 => 2000,
small => [0, 1,  500, 1, 1000, 0                  ],
med   => [       500, 0, 1000, 1, 1500, 0         ],
huge  => [               1000, 0, 1500, 1, 2000, 1],
);
my \$cap  = \$fe->new_variable( 0 => 1800,
avg   => [0, 1, 1500, 1, 1700, 0         ],
high  => [      1500, 0, 1700, 1, 1800, 1],
);
# internal variables need sets, but no membership functions
my \$saturation = \$fe->new_variable( # from => to may be ommitted
low   => [],
crit  => [],
over  => [],
);
# But output variables need membership functions for their sets:
my \$green = \$fe->new_variable( -5 => 5,
decrease => [-5, 1, -2, 1, 0, 0            ],
ok       => [       -2, 0  0, 1, 2, 0      ],
increase => [              0, 0, 2, 1, 5, 1],
);

# Reset FuzzyEngine (resets all variables)
\$fe->reset();

# Reset a fuzzy variable directly
\$flow->reset;

# Fuzzification of input variables
\$flow->fuzzify( 600 );
\$cap->fuzzify( 1000 );

# Membership degrees of the respective sets are now available:
my \$flow_is_small = \$flow->small(); # 0.8
my \$flow_is_med   = \$flow->med();   # 0.2
my \$flow_is_huge  = \$flow->huge();  # 0.0

# RULES and their application

# a) first step, result is \$saturation, an intermediate set
# 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) second step, deduce output variable from internal state of saturation
\$green->decrease( \$saturation->low()  );
\$green->ok(       \$saturation->crit() );
\$green->increase( \$saturation->over() );

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

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

# EXPORT

Nothing is exported or exportable.

# 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, and there should be no need to defuzzify variables just to compute any first variables.

Credits to Ala Qumsieh and his 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.

## Fuzzy stuff

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

`\$fe->or( ... )` (Disjunction)

Maximum of membership degrees

`\$fe->and( ... )` (Conjunction)

Minimum of membership degrees

`\$fe->not( \$var->\$set )` (Negation)

1-degree of membership

Aggregation of rules (Disjunction)

Maximum

Defuzzification is based on

Implication

Clip membership function of a set according to membership degree, before the implicated memberships of all sets of a variable are taken for defuzzification:

Defuzzification

Centroid of aggregated (and clipped) membership functions

## Public functions

Creation of an `AI::FuzzyEngine` object by

`    my \$fe = AI::FuzzyEngine->new();`

This function has no parameters, but provides the fuzzy methods `or`, `and` and `not`, as listed above. I plan to introduce alternative fuzzy operations, they will be configured as arguments to `new`.

Once created, the engine can create fuzzy variables by `new_variable`:

```    my \$var = \$fe->new_variable( \$from => \$to,
\$name_of_set1 => [\$x11, \$y11, \$x12, \$y12, ... ],
\$name_of_set2 => [\$x21, \$y21, \$x22, \$y22, ... ],
...
);```

Result is an AI::FuzzyEngine::Variable. The name_of_set strings are taken to assign corresponding methods for the respective fuzzy variables. They must be valid function identifiers.

Fuzzy variables provide a method to fuzzify input values:

`    \$var->fuzzify( \$val );`

according to the defined sets and their membership functions.

The memberships of the sets of \$var are accessible by the respective functions:

`    my \$membership_degree = \$var->\$name_of_set();`

Memberships can be assigned directly (within rules for example):

`    \$var->\$name_of_set( \$membership_degree );`

If multiple membership_degrees are given, they are "anded":

`    \$var->\$name_of_set( \$degree1, \$degree2, ... ); # "and"`

By this, simple rules can be coded directly:

`    my \$var_3->zzz( \$var_1->xxx, \$var_2->yyy, ... ); # "and"`

this implements the fuzzy implication

`    if \$var_1->xxx and \$var_2->yyy and ... then \$var_3->zzz`

The membership degrees of a variable's sets can be reset to undef:

```    \$var->reset(); # resets a variable
\$fe->reset();  # resets all variables```

The fuzzy engine `\$fe` has all variables registered that have been created by its `new_variable` method.

A variable can be defuzzified:

`    my \$out_value = \$var->defuzzify();`

Sometimes internal variables are used that need neither fuzzification nor defuzzification. They can be created by a simplified call to `new_variable`:

```    my \$var_int = \$fe->new_variable( \$name_of_set1 => [],
\$name_of_set2 => [],
...
);```

Hence, they can not use the methods `fuzzify` or `defuzzify`.

Fuzzy operations are simple operations on floating values between 0 and 1:

```    my \$conjunction = \$fe->and( \$var1->xxx, \$var2->yyy, ... );
my \$disjunction = \$fe->or(  \$var1->xxx, \$var2->yyy, ... );
my \$negated     = \$fe->not( \$var1->zzz );```

There is no magic.

A sequence of rules for the same set can be implemented as follows:

```    \$var_3->zzz( \$var_1->xxx, \$var_2->yyy, ... );
\$var_3->zzz( \$var_4->aaa, \$var_5->bbb, ... );```

The subsequent application of `\$var_3->zzz(...)` corresponds to "or" operations (aggregation of rules).

Only a reset can reset `\$var_3`.

## Todos

Add optional alternative implementations of fuzzy operations
More checks on input arguments and allowed method calls
Make the module PDL aware
Split tests into API tests and test of internal functions

# CAVEATS / BUGS

This is my first module. I'm happy about feedback that helps me to learn and improve my contributions to the Perl ecosystem.

Please report any bugs or feature requests to `bug-ai-fuzzyengine at rt.cpan.org`, or through the web interface at http://rt.cpan.org/NoAuth/ReportBug.html?Queue=AI-FuzzyEngine. I will be notified, and then you'll automatically be notified of progress on your bug as I make changes.

# SUPPORT

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

`    perldoc AI::FuzzyEngine`

You can also look for information at:

# AUTHOR

Juergen Mueck, jurgen.muck@yahoo.de