zeta-methods {kappalab} | R Documentation |
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.
Returns an object of class capacity
.
Returns an object of class card.set.func
.
Returns an object of class game
.
Returns an object of class 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.
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
.
## 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)