Mobius-methods {kappalab} | R Documentation |
Computes the Möbius transform of a set function. The Möbius transform is the inverse of the zeta transform.
Returns an object of class Mobius.capacity
.
Returns an object of class Mobius.card.set.func
.
Returns an object of class Mobius.game
.
Returns an object of class Mobius.set.func
.
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.
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
.
## 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))