scales

This module gathers all data scales and their features.

class DiscreteQuantitativeScale(values, preference_direction=None, **kwargs)

Bases: QuantitativeScale

Class for discrete quantitative scale.

Parameters

values (List[float]) – numeric values that constitute the scale
preference_direction (Union[PreferenceDirection, None]) –

static binary()

Return binary scale.

Returns
Return type: DiscreteQuantitativeScale

classmethod fit(data, preference_direction=None, **kwargs)

Create a scale that fits the data.

Parameters

data (Series) –
preference_direction (Optional[PreferenceDirection]) –

Returns

scale

Raises

TypeError – if data is not numeric

Return type

Self

property interval: Interval: Return interval on which scale is defined.

is_better(x, y)

Check if x is better than y according to this scale.

Parameters

x (Any) –
y (Any) –

Returns

Return type

bool

is_better_or_equal(x, y)

Check if x is better or equal to y according to this scale

Parameters

x (Any) –
y (Any) –
scale –

Returns

Return type

bool

label(x)

Return scale value corresponding to given number.

Parameters: x (float) –
Returns
Raises: ValueError – if x is outside scale
Return type: Any

static normal()

Return normal scale.

Returns
Return type: QuantitativeScale

property numeric: QuantitativeScale: Return corresponding numeric scale.

range(nb=None)

Return range of value from scale.

Parameters: nb (Optional[int]) – number of values to return
Returns
Return type: List

value(x)

Return corresponding numeric value.

Parameters: x (Any) –
Returns
Raises: ValueError – if x is outside scale
Return type: float

class FuzzyScale(fuzzy, preference_direction=None, defuzzify_method='centre_of_gravity', **kwargs)

Bases: QualitativeScale

This class implements a MCDA fuzzy qualitative scale.

Parameters

fuzzy (Series) –
preference_direction (Union[PreferenceDirection, None]) –
defuzzify_method (str) –

Raises

TypeError –

if fuzzy contains non-fuzzy numbers

defuzzify(method=None)

Defuzzify all fuzzy numbers using given method.

Parameters: method (Optional[str]) – method used to defuzzify (from mcda.core.functions.FuzzyNumber numeric methods)
Return type: Series

classmethod fit(data, preference_direction=None, **kwargs)

Create a scale that fits the data.

Parameters

data (Series) –
preference_direction (Optional[PreferenceDirection]) –

Returns

scale

Return type

Self

fuzziness(fuzzy)

Returns the fuzziness of given fuzzy number w.r.t this scale.

Parameters: fuzzy (FuzzyNumber) –
Returns
Return type: float

property interval: Interval: Return interval on which scale is defined.

is_better(x, y)

Check if x is better than y according to this scale.

Parameters

x (Any) –
y (Any) –

Returns

Return type

bool

is_better_or_equal(x, y)

Check if x is better or equal to y according to this scale

Parameters

x (Any) –
y (Any) –
scale –

Returns

Return type

bool

property is_fuzzy_partition: bool

Test whether the scale define a fuzzy partition.

Returns

label(x)

Return label associated to given number.

Parameters: x (float) –
Raises: ValueError – if x corresponds to no label
Returns: most probable label associated to given value
Return type: Any

property numeric: QuantitativeScale: Return corresponding numeric scale.

ordinal_distance(a, b)

Returns the ordinal distance between the labels (sorted by defuzzified values).

Parameters

a (Any) –
b (Any) –

Returns

Raises

ValueError – if a or b is not inside the scale

Return type

float

range(nb=None)

Return range of value from scale.

Parameters: nb (Optional[int]) – number of values to return (always ignored here)
Returns
Return type: List

similarity(fuzzy1, fuzzy2)

Returns similarity between both fuzzy numbers w.r.t this scale.

Parameters

fuzzy1 (FuzzyNumber) –
fuzzy2 (FuzzyNumber) –

Returns

Return type

float

Note

implementation based on [IMVM10]

specificity(fuzzy)

Returns the specificity of given fuzzy number w.r.t this scale.

Parameters: fuzzy (FuzzyNumber) –
Returns
Return type: float

Todo

check whether normalization should be done before computing area

value(x)

Return corresponding numeric value.

Parameters: x (Any) –
Returns
Return type: float

MAX = PreferenceDirection.MAX: User-friendly way to call PreferenceDirection.MAX

MIN = PreferenceDirection.MIN: User-friendly way to call PreferenceDirection.MIN

class NominalScale(labels, **kwargs)

Bases: Scale

This class implements a MCDA nominal scale.

Parameters: labels (List) –

classmethod fit(data, **kwargs)

Create a scale that fits the data.

Parameters: data (Series) –
Returns: scale
Return type: NominalScale

is_better(x, y)

Check if x is better than y according to this scale.

Parameters

x (Any) –
y (Any) –

Returns

Raises

TypeError – if scale is not ordinal

Return type

bool

is_better_or_equal(x, y)

Check if x is better or equal to y according to this scale

Parameters

x (Any) –
y (Any) –
scale –

Returns

Return type

bool

range(nb=None)

Return range of value from scale.

Parameters: nb (Optional[int]) – number of values to return (always ignored here)
Returns
Return type: List

class PreferenceDirection(value)

Bases: Enum

Enumeration of MCDA preference directions.

MAX = 'MAX'

MIN = 'MIN'

classmethod content_message()

Return list of items and their values.

Returns
Return type: str

classmethod has_value(x)

Check if value is in enumeration.

Parameters: x (PreferenceDirection) –
Returns
Return type: bool

class QualitativeScale(values, preference_direction=None, **kwargs)

Bases: OrdinalScale, NominalScale

This class implements a MCDA qualitative scale.

Parameters

values (Series) – numeric series with labels as index
preference_direction (Union[PreferenceDirection, None]) –

Raises

TypeError –

if values contains non-numeric values

Warning

This scale contains labels not values. values are only here to define a corresponding quantitative scale for default scale transformation. After calling transform_to() with no associated scale, the data is no longer considered inside the qualitative scale.

classmethod fit(data, preference_direction=None, **kwargs)

Create a scale that fits the data.

Parameters

data (Series) –
preference_direction (Optional[PreferenceDirection]) –

Returns

scale

Return type

Self

property interval: Interval: Return interval on which scale is defined.

is_better(x, y)

Check if x is better than y according to this scale.

Parameters

x (Any) –
y (Any) –

Returns

Return type

bool

is_better_or_equal(x, y)

Check if x is better or equal to y according to this scale

Parameters

x (Any) –
y (Any) –
scale –

Returns

Return type

bool

label(x)

Return label corresponding to given number.

Parameters: x (float) –
Raises: ValueError – if x corresponds to no label
Returns
Return type: Any

property numeric: QuantitativeScale: Return corresponding numeric scale.

range(nb=None)

Return range of value from scale.

Parameters: nb (Optional[int]) – number of values to return (always ignored here)
Returns
Return type: List

value(x)

Return corresponding numeric value.

Parameters: x (Any) –
Returns
Return type: float

class QuantitativeScale(arg1=-inf, dmax=inf, min_in=True, max_in=True, preference_direction=None, **kwargs)

Bases: OrdinalScale

Class for quantitative scale (interval based).

Parameters

arg1 (Union[float, Interval]) – min boundary of scale or complete interval
dmax (float) – max boundary of scale (only considered if arg1 type is not interval)
min_in (bool) – is min boundary inside scale or not
max_in (bool) – is max boundary inside scale or not
preference_direction (Union[PreferenceDirection, None]) –

Raises

ValueError – if dmin bigger than dmax

classmethod fit(data, preference_direction=None, **kwargs)

Create a scale that fits the data.

Parameters

data (Series) –
preference_direction (Optional[PreferenceDirection]) –

Returns

scale

Raises

TypeError – if data is not numeric

Return type

Self

property interval: Interval: Return interval on which scale is defined.

is_better(x, y)

Check if x is better than y according to this scale.

Parameters

x (Any) –
y (Any) –

Returns

Return type

bool

is_better_or_equal(x, y)

Check if x is better or equal to y according to this scale

Parameters

x (Any) –
y (Any) –
scale –

Returns

Return type

bool

label(x)

Return scale value corresponding to given number.

Parameters: x (float) –
Returns
Raises: ValueError – if x is outside scale
Return type: Any

static normal()

Return normal scale.

Returns
Return type: QuantitativeScale

property numeric: QuantitativeScale: Return corresponding numeric scale.

range(nb=None)

Return range of value from scale.

Parameters: nb (Optional[int]) – number of values to return
Returns
Return type: List

value(x)

Return corresponding numeric value.

Parameters: x (Any) –
Returns
Raises: ValueError – if x is outside scale
Return type: float

common_scale_type(scale_types)

Determine common type between scale types.

Parameters: scale_types (List[Type[S]]) –
Returns: common scale type
Return type: Type[S]