normalize-methods: Normalizes a capacity.

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Normalizes a capacity.

Description

Returns the normalized version of a capacity. The capacity can be given either under the form of an object of class capacity, card.capacity or Mobius.capacity. In the case of objects of class capacity and card.capacity, the normalization is performed by dividing each coefficient of the capacity by the value of the capacity on the universe. In the case of objects of class Mobius.capacity, the normalization is performed by dividing each coefficient of the Möbius transform by the sum of all the coefficients.

Methods

object = "Mobius.capacity"

Returns an object of class Mobius.capacity.

object = "capacity"

Returns an object of class capacity.

object = "card.capacity"

Returns an object of class card.capacity.

See Also

capacity-class,
Mobius.capacity-class,
card.capacity-class,
Mobius-methods,
is.normalized-methods.

Examples

## a capacity
mu <- capacity(0:15)

## normalize it
is.normalized(mu)
normalize(mu)

## a similar example with a Mobius.capacity object
a <- Mobius(mu)
is.normalized(a)
normalize(a)
zeta(normalize(a))

## a similar example with a card.capacity object
mu <- card.capacity(0:6)
is.normalized(mu)
normalize(mu)
Mobius(normalize(mu))

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