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

 capacity-class R Documentation

## 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 = 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

```## 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 Feb. 16, 2023, 8:42 p.m.