# capacity-class: Class "capacity" In kappalab: Non-Additive Measure and Integral Manipulation Functions

## 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")`

`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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29``` ```## 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) ```

kappalab documentation built on May 2, 2019, 5:49 a.m.