Mobius.game-class {kappalab} | R Documentation |
Class representing the Möbius transform of a game.
Objects can be created by calls to the function Mobius.game
.
n
:Object of class numeric
of length 1 containing the
number of elements of the set on which the Möbius transform is
defined.
k
:Object of class numeric
of length 1 containg the order
of truncation of the Möbius transform: subsets whose cardinal is
superior to k are considered to be zero.
subsets
:Object of class numeric
containing
the "k
power set" of the underlying
set in "natural" order . The subsets are encoded as integers.
data
:Object of class numeric
of length
choose(n,0) + ... + choose(n,k)
representing the
coefficients of a truncated Möbius transform of a game in "natural" order.
Class Mobius.set.func
, directly.
Class superclass.set.func
, by class Mobius.set.func
.
signature(object = "Mobius.game", f =
"numeric")
signature(object = "Mobius.game", f =
"numeric")
signature(object = "Mobius.game", f =
"numeric")
signature(object = "Mobius.game")
game-class
,
Mobius.game
,
Choquet.integral-methods
,
Sipos.integral-methods
,
Sugeno.integral-methods
,
zeta-methods
,
expect.Choquet.norm-methods
.
## a game (which is a capacity) mu <- game(c(0,rep(1,15))) ## and its Mobius representation a <- Mobius(mu) # the attributes of object a a@n a@k a@data a@subsets ## a transformation zeta(a) ## let us check ... Mobius(zeta(a)) ## integral calculations f <- c(0.2,0.3,0.1,0.7) Choquet.integral(a,f) Sugeno.integral(a,f) f <- c(0.2,-0.3,0.1,-0.7) Sipos.integral(a,f)