interaction.indices-methods {kappalab} | R Documentation |
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
.
The Shapley interaction indices are computed from the Möbius transform of a set function.
The Shapley interaction indices are computed from a cardinal set function.
The Shapley interaction indices are computed from a general set function.
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.
Mobius.set.func-class
,
card.set.func-class
,
set.func-class
,
Mobius-methods
.
## 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)