Aggregated

Aggregated

Bases: Term

Special term that represents a fuzzy set of activated terms to mainly serve as the fuzzy output value of output variables.

Equation

\(\mu(x)=\bigoplus_i^n\alpha_i\otimes\mu_i(x) = \alpha_1\otimes\mu_1(x) \oplus \ldots \oplus \alpha_n\otimes\mu_n(x)\)

where

• \(\alpha_i\): activation degree of term \(i\)
• \(\mu_i\): membership function of term \(i\)
• \(\otimes\): implication operator
• \(\oplus\): aggregation operator

related

• fuzzylite.term.Activated
• fuzzylite.variable.OutputVariable
• fuzzylite.rule.Antecedent
• fuzzylite.rule.Rule
• fuzzylite.term.Term

Attributes

aggregation instance-attribute

aggregation = aggregation

maximum instance-attribute

maximum = maximum

minimum instance-attribute

minimum = minimum

terms instance-attribute

terms = list(terms or [])

Functions

__init__

__init__(
    name: str = "",
    minimum: float = nan,
    maximum: float = nan,
    aggregation: SNorm | None = None,
    terms: Iterable[Activated] | None = None,
) -> None

Constructor.

Parameters:

Name	Type	Description	Default
name	str	name of the aggregated term	''
minimum	float	minimum value of the range of the fuzzy set	nan
maximum	float	maximum value of the range of the fuzzy set	nan
aggregation	SNorm | None	aggregation operator	None
terms	Iterable[Activated] | None	list of activated terms	None

__repr__

__repr__() -> str

Return the code to construct the term in Python.

Returns:

Type	Description
str	code to construct the term in Python.

activation_degree

activation_degree(term: Term) -> Scalar

Compute the aggregated activation degree of the term.

Parameters:

Name	Type	Description	Default
term	Term	term to compute the aggregated activation degree	required

Returns:

Type	Description
Scalar	aggregated activation degree for the term.

clear

clear() -> None

Clear the list of activated terms.

grouped_terms

grouped_terms() -> dict[str, Activated]

Group the activated terms and aggregate their activation degrees.

Returns:

Type	Description
dict[str, Activated]	grouped activated terms by name with aggregated activation degrees.

related

• fuzzylite.defuzzifier.WeightedSum
• fuzzylite.defuzzifier.WeightedAverage

highest_activated_term

highest_activated_term() -> Activated | None

Find the term with the maximum aggregated activation degree.

Returns:

Type	Description
Activated | None	term with the maximum aggregated activation degree.

Raises:

Type	Description
ValueError	when working with vectorization (eg, size(activation_degree) > 1)

membership

membership(x: Scalar) -> Scalar

Aggregate the activated terms' membership function values of \(x\) using the aggregation operator.

Parameters:

Name	Type	Description	Default
x	Scalar	scalar	required

Returns:

Type	Description
Scalar	\(\mu(x)=\bigoplus_i^n\alpha_i\otimes\mu_i(x) = \alpha_1\otimes\mu_1(x) \oplus \ldots \oplus \alpha_n\otimes\mu_n(x)\)

parameters

parameters() -> str

Return the space-separated parameters of the term.

Returns:

Type	Description
str	aggregation minimum maximum terms

range

range() -> float

Return the magnitude of the range of the fuzzy set.

Returns:

Type	Description
float	maximum - minimum