Mobius-methods {kappalab} | R Documentation |
The Möbius transform
Description
Computes the Möbius transform of a set function. The Möbius transform is the inverse of the zeta transform.
Methods
- object = "capacity"
Returns an object of class
Mobius.capacity
.- object = "card.set.func"
Returns an object of class
Mobius.card.set.func
.- object = "game"
Returns an object of class
Mobius.game
.- object = "set.func"
Returns an object of class
Mobius.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
Mobius.capacity-class
,
Mobius.card.set.func-class
,
Mobius.game-class
,
Mobius.set.func-class
,
capacity-class
,
card.set.func-class
,
game-class
,
set.func-class
,
zeta-methods
.
Examples
## a capacity
mu <- capacity(0:15)
mu
## its Mobius transform
a <- Mobius(mu)
a
## its zeta transform
zeta(a)
## a similar example with a game object
mu <- game(c(0,-2:12))
mu
Mobius(mu)
zeta(Mobius(mu))
## a similar example with a set.func object
mu <- set.func(-7:8)
mu
Mobius(mu)
zeta(Mobius(mu))
## a similar example with a card.set.func object
mu <- card.set.func(-3:4)
mu
Mobius(mu)
zeta(Mobius(mu))