Mobius.set.func-class: Class "Mobius.set.func"

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Class "Mobius.set.func"

Description

Class representing the Möbius transform of a set function.

Objects from the Class

Objects can be created by calls to the function Mobius.set.func.

Slots

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 set function in "natural" order.

Extends

Class superclass.set.func, directly.

Methods

show

signature(object = "Mobius.set.func")

as.Mobius.card.set.func

signature(object = "Mobius.set.func")

as.card.set.func

signature(object = "Mobius.set.func")

as.set.func

signature(object = "Mobius.set.func")

as.Mobius.game

signature(object = "Mobius.set.func")

as.Mobius.capacity

signature(object = "Mobius.set.func")

interaction.indices

signature(object = "Mobius.set.func")

is.cardinal

signature(object = "Mobius.set.func")

is.kadditive

signature(object = "Mobius.set.func", k = "numeric")

is.monotone

signature(object = "Mobius.set.func")

k.truncate.Mobius

signature(object = "Mobius.set.func", k = "numeric")

Shapley.value

signature(object = "Mobius.set.func")

to.data.frame

signature(object = "Mobius.set.func")

zeta

signature(object = "Mobius.set.func")

See Also

set.func-class,
Mobius.set.func,
as.Mobius.card.set.func-methods,
as.card.set.func-methods,
as.set.func-methods,
as.Mobius.game-methods,
as.Mobius.capacity-methods,
interaction.indices-methods,
is.cardinal-methods,
is.kadditive-methods,
is.monotone-methods,
k.truncate.Mobius-methods,
Shapley.value-methods,
to.data.frame-methods,
zeta-methods.

Examples

## the Mobius transform of a set function directly
a <- Mobius.set.func(1:16,4,4)

## the attributes of the object
a@n
a@k
a@data
a@subsets

## a set function
mu <- set.func(7:-8)
## and its Mobius transform
a <- Mobius(mu)

## some conversions that cannot work
## as.game(a)
## as.capacity(a)
## as.card.set.func(a)

## some tests
is.cardinal(a)
is.kadditive(a,2)
is.monotone(a)

## some transformations
zeta(a)
k.truncate.Mobius(a,2)

## summary 
Shapley.value(a)
interaction.indices(a)
# the same
summary(a)

## save the Mobius transform to a file
d <- to.data.frame(a)
## Not run: write.table(d,"my.Mobius.set.func.csv",sep="\t")

# finally, some conversions that should work
mu <- set.func(c(0,1,1,1,2,2,2,3))
a <- Mobius(mu)
as.Mobius.game(a)
as.Mobius.capacity(a)
as.Mobius.card.set.func(a)

kappalab documentation built on Nov. 8, 2023, 1:07 a.m.