capacity-class {kappalab}

Class "capacity"

Description

Class representing a capacity, i.e. a monotone set function vanishing at the empty set (also called fuzzy measure, non-additive measure, monotone measure).

Objects from the Class

Objects can be mainly created by calls to the functions capacity and entropy.capa.ident.

Slots

n:

Object of class numeric of length 1 equal to the number of elements of the set on which the capacity is defined.

subsets:

Object of class numeric of length 2^n containing the power set of the underlying set in "natural" order. The subsets are coded as integers.

data:

Object of class numeric of length 2^n containing the coefficients of the capacity in binary order. We necessarily have data[1] = 0 plus some additional monotonicity constraints.

Extends

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

Methods

as.card.capacity

signature(object = "capacity")

conjugate

signature(object = "capacity")

entropy

signature(object = "capacity")

favor

signature(object = "capacity")

is.normalized

signature(object = "capacity")

normalize

signature(object = "capacity")

Mobius

signature(object = "capacity")

orness

signature(object = "capacity")

variance

signature(object = "capacity")

veto

signature(object = "capacity")

See Also

capacity,
entropy.capa.ident,
as.card.capacity-methods,
conjugate-methods,
entropy-methods,
favor-methods,
is.normalized-methods,
normalize-methods,
Mobius-methods,
orness-methods,
variance-methods,
veto-methods.

Examples

## a capacity
mu <- capacity(c(0:13,13,13)/13)

## the attributes of the object
mu@n
mu@data
mu@subsets

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

## a conversion that should not work
## as.card.capacity(mu)

## some transformations
conjugate(mu)
Mobius(mu)
## let us check ...
zeta(Mobius(mu))

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