set_functions

This module gathers classes defining set functions.

class ISetFunction(values, ensemble=None, validate=True)

Bases: ABC

This class represents a set function.

Parameters

  • values (Union[List, Dict, ISetFunction]) –

    values of the function as either:

    • a list ordered as a binary mask on the ensemble

    • a dictionary with HashableSet as keys

    • another SetFunction object (used for casting)

  • ensemble (Union[List, None]) – ensemble from which to build the set (its default value is \(\mathbf{Z}^+\))

  • validate (bool) – if True, raises an error when building an invalid instance

__call__(*args, **kwargs)

Call this set function on the set composed of all provided arguments

Returns

value

property as_capacity: Self

Return the instance if it respects its properties.

The properties are the following:

  • the set function is defined on a power set

  • the set function is a game

  • the set function is monotonous

  • the set function is normal

Raises

  • KeyError –

    • if set function is not defined on a power set

  • ValueError –

    • if set function is not a game

    • if set function is not monotonous

    • if set function is not normal

property ensemble: List

Return a copy of the ensemble of this set function.

Returns

property interaction_index: DataFrame

Return interaction index matrix.

Returns

Note

Formula is based on [GKM08].

property is_additive: bool

Check if the set function is additive or not.

Check that \(\forall S, T \subseteq N, S \cap T = \emptyset, \mu(S \cup T) = \mu(S) + \mu(T)\)

Returns

Note

use math.isclose() to add tolerance

property is_capacity: bool

Check if the instance is a capacity.

The properties are the following:

  • the set function is defined on a power set

  • the set function is a game

  • the set function is monotonous

  • the set function is normal

Returns

True if instance is a capacity, False otherwise

property is_cardinality_based: bool

Check if the set function is cardinality-based.

Check that \(\forall T \subseteq N, \mu(T)\) only depends on T cardinality.

Returns

Note

use math.isclose() to add tolerance

property is_game: bool

Check if the set function is a game.

Check \(\nu(\emptyset) = 0\)

Returns

property is_monotonous: bool

Check if the set function is monotonous.

Check that \(\forall S, T \subseteq N, S \subseteq T \Rightarrow \nu(S) \leq \nu(T)\)

Returns

Note

use math.isclose() to add tolerance

property is_normal: bool

Check if the set function is normalized.

Check set_function is a capacity, and that \(\nu(N) = 1\)

Returns

Note

use math.isclose() to add tolerance

property is_powerset_function: bool

Check if the set function is defined on a power set.

Check length of set_function is a power of 2.

Returns

property shapley: Series

Return Shapley values.

Returns

Note

Formula is based on [GKM08].

property size: int

Return the size of the ensemble of this set function.

Returns

property values: Dict

Return a copy of the dictionary defining this set function.

Returns