zeta-methods {kappalab} | R Documentation |
The zeta transform
Description
Computes the zeta transform of a set function given under the form of its Möbius transform. The zeta transform is the inverse of the Möbius transform.
Methods
- object = "Mobius.capacity"
Returns an object of class
capacity
.- object = "Mobius.card.set.func"
Returns an object of class
card.set.func
.- object = "Mobius.game"
Returns an object of class
game
.- object = "Mobius.set.func"
Returns an object of class
set.func
.
References
G-C. Rota (1964), On the foundations of combinatorial theory. I. Theory of Möbius functions, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, pages 340-368.
A. Chateauneuf and J-Y. Jaffray (1989), Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Mathematical Social Sciences 17, pages 263-283.
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
capacity-class
,
card.set.func-class
,
game-class
,
set.func-class
,
Mobius.capacity-class
,
Mobius.card.set.func-class
,
Mobius.game-class
,
Mobius.set.func-class
,
Mobius-methods
.
Examples
## the Mobius transform of a capacity
a <- Mobius.capacity(c(rep(0,15),1),4,4)
a
## its zeta transform
zeta(a)
## let us check
Mobius(zeta(a))
## a similar example with a Mobius.card.set.func object
mu <- card.set.func(-3:4)
a <- Mobius(mu)
zeta(a)