Term

class floulib.Term(*args)

Bases: Plot

This class contains methods to define and use a term for linguistic variable, especially for rules in fuzzy controller. In general, a term is the association of a string like “small” and its meaning, i.e. the membership function associated with the term.

In special cases, variable may contain purely linguistic terms which have no meaning associated with.

Note

Term is a subclass of Plot, therefore all methods in Plot may be used.

prototype = None

Prototype associated with the term to be used in the symbolic defuzzification (method WAM-P). The prototype can be:

• a scalar,

• a list of scalars,

• a dict containing scalar or list of scalars.

__init__(*args)

Constructor

Parameters:

*args (str | Multilinear) –

• If the type of args is str, args defines the name of the term.

• If args is Multilinear, args defines the meaning of the term.

Raises:

• Exception – Raised if the number of positional arguments is equal to 0 or greater than 2.

• TypeError – Raised if there is one positional argument which is not an instance of str.

Return type:

None.

Example

Generates the term A as the association of the Singleton(‘A’) and its meaning provided by the LR fuzzy subset LR(1, 0.5, 0.5).

>>> from floulib import Term
>>> A = Term('A', LR(1, 0.5, 0.5))

Same as above

>>> A = Term(LR(1, 0.5, 0.5), 'A')

Creates the term A as the Singleton(‘A’) with no meaning.

>>> A = Term('A')

area()

Area of the meaning of the term (see floulib.LR.area()).

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of LR.

Returns:

The area.

Return type:

float

centroid()

Centroid of the meaning of the term (see floulib.LR.centroid()).

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of LR.

Returns:

The centroid.

Return type:

float

membership(x)

Computes the grade of membership to the meaning for x (see floulib.Multilinear.membership()).

Parameters:

x (float) – Point where the grade of membership is computed.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

Grade of membership.

Return type:

float

mode()

Mode of the meaning of the term (see floulib.LR.mode()).

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of LR.

Returns:

The mode.

Return type:

float

necessity(dpi)

Computes the necessity of the meaning of the term knowing the distribution of possibility dpi (see floulib.Multilinear.necessity()).

Parameters:

dpi (Multilinear) – The possibility distribution.

Raises:

TypeError – Raised by the private method Term._get_meaning() if the parameter is not an instance of Term or Multilinear.

Returns:

The necessity.

Return type:

Multilinear

possibility(dpi)

Computes the possibility of the meaning of the term knowing the distribution of possibility dpi (see floulib.Multilinear.possibility()).

Parameters:

dpi (Multilinear) – The possibility distribution.

Raises:

TypeError – Raised by the private method Term._get_meaning() if the parameter is not an instance of Term or Multilinear.

Returns:

The possibility.

Return type:

Multilinear

Certainty(level)

Adds a certainty level to the meaning of a term (see floulib.Multilinear.Certainty()).

Parameters:

level (float) – The certainty level.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The multilinear fuzzy subset with certainty level.

Return type:

Multilinear

Uncertainty(level)

Adds an uncertainty level to the meaning of a term (see floulib.Multilinear.Uncertainty()).

Parameters:

level (float) – The uncertainty level.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The multilinear fuzzy subset with uncertainty level.

Return type:

Multilinear

__and__(other)

Special method for using the operator & between two instances of Term. It returns the intersection of the meanings of the terms (see floulib.Multilinear.__and__()).

Parameters:

other (Term) – The RHS operand.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The intersection of the meanings.

Return type:

Multilinear

__invert__()

Special method for using the unary operator ~ as the complement of a term (see floulib.Multilinear.__invert__()).

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The complement of the meaning.

Return type:

Multilinear

__neg__()

Special method for using the unary operator - as the opposite of a term (see floulib.Multilinear.__neg__()).

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The opposite of the meaning.

Return type:

Multilinear

__or__(other)

Special method for using the operator | between two instances of Term. It returns the union of the meanings of the terms (see floulib.Multilinear.__or__()).

Parameters:

other (Term) – The RHS operand.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The union of the meanings.

Return type:

Multilinear

__rmul__(other)

Special method for using the opertor * with a number as the LHS operand. Its multiplies the grades of membership of themeaning of the term by the LHS operand and truncates them to 1 (see floulib.Multilinear.__rmul__()).

Parameters:

other (Term) – The RHS operand.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The result.

Return type:

Multilinear

__xor__(other)

Special method for using the opertor ^ between two instances of Term. It returns the symmetric difference of the meanings of the terms (see floulib.Multilinear.__xor__()).

Parameters:

other (Term) – The RHS operand.

Raises:

TypeError – Raised is the meaning associated with the term is not an instance of Multilinear.

Returns:

The symmetric difference of the meanings.

Return type:

Multilinear