Mobius.capacity-class: Class "Mobius.capacity"

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Class "Mobius.capacity"

Description

Class representing the Möbius transform of a capacity.

Objects from the Class

Objects can be mainly created by calls to the functions Mobius.capacity,
mini.var.capa.ident, ls.sorting.capa.ident, and least.squares.capa.ident.

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: the value of subsets whose cardinal is superior to k is put to 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 capacity in "natural" order.

Extends

Class Mobius.game, directly. Class superclass.capacity, directly.
Class Mobius.set.func, by class Mobius.game. Class superclass.set.func, by class Mobius.game.

Methods

entropy

signature(object = "Mobius.capacity")

favor

signature(object = "Mobius.capacity")

is.normalized

signature(object = "Mobius.capacity")

normalize

signature(object = "Mobius.capacity")

orness

signature(object = "Mobius.capacity")

variance

signature(object = "Mobius.capacity")

veto

signature(object = "Mobius.capacity")

zeta

signature(object = "Mobius.capacity")

See Also

capacity-class,
entropy-methods,
favor-methods,
is.normalized-methods,
orness-methods,
variance-methods,
veto-methods,
zeta-methods,
mini.var.capa.ident,
least.squares.capa.ident,
ls.sorting.capa.ident.

Examples

## a capacity
mu <- capacity(c(0,0,0:13))
## and its Mobius representation
a <- Mobius(mu)
a

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

## a test
is.normalized(a)
## normalize it
normalize(a)

## a transformation
zeta(a)
## Let us check ...
Mobius(zeta(a))

## some summary indices
orness(a)
veto(a)
favor(a)
variance(a)
entropy(a)
## the same
summary(a)

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