capacity-class | R Documentation |

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 can be mainly created by calls
to the functions `capacity`

and `entropy.capa.ident`

.

`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.

Class `game`

, directly.
Class `superclass.capacity`

, directly.
Class `set.func`

, by class `game`

.
Class `superclass.set.func`

, by class `game`

.

- 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`

.

```
## 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)
```

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