kappalab (version 0.4-7)

interaction.indices-methods: The Shapley interaction indices

Description

Computes the Shapley interaction index for pairs of elements with respect to a set function. The set function can be given either under the form of an object of class set.func, card.set.func or Mobius.set.func .

Methods

object = "Mobius.set.func"

The Shapley interaction indices are computed from the Mbius transform of a set function.

object = "card.set.func"

The Shapley interaction indices are computed from a cardinal set function.

object = "set.func"

The Shapley interaction indices are computed from a general set function.

References

G. Owen (1971/72), Multilinear extensions of games, Management Sci. 18, pages 64--79. T. Murofushi and S. Soneda (1993), Techniques for reading fuzzy measures (III): interaction index, 9th Fuzzy System Symposium, pages 693--696, Saporo, Japan.

M. Grabisch, J-L. Marichal and M. Roubens (2000), Equivalent representations of set functions, Mathematics of Operations Research 25(2), pages 157--178.

See Also

Mobius.set.func-class, card.set.func-class, set.func-class, Mobius-methods.

Examples

## a set function
mu <- set.func(c(-7:6,6,6))

## the associated interaction indices
interaction.indices(mu)


## a similar example using a Mobius.set.func object
a <- Mobius(mu)
interaction.indices(a)

## a similar example using a card.set.func object
mu <- upper.capacity(6)
interaction.indices(mu)