game-class | R Documentation |

Class representing a game, i.e. a set function vanishing at
the empty set (also called *non monotonic fuzzy measure*).

Objects can be created by calls to the function `game`

.

`n`

:Object of class

`numeric`

of length 1 equal to the number of elements of the set on which the game 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 game in binary order. We necessarily have`data[1] = 0`

.

Class `set.func`

, directly.
Class `superclass.set.func`

, by class `set.func`

.

- as.card.game
`signature(object = "game")`

- Choquet.integral
`signature(object = "game", f = "numeric")`

- Mobius
`signature(object = "game")`

- Sipos.integral
`signature(object = "game", f = "numeric")`

- Sugeno.integral
`signature(object = "game", f = "numeric")`

- pdf.Choquet.unif
`signature(object = "game", f = "numeric")`

- cdf.Choquet.unif
`signature(object = "game", f = "numeric")`

- expect.Choquet.unif
`signature(object = "game")`

- sd.Choquet.unif
`signature(object = "game")`

- expect.Choquet.norm
`signature(object = "game")`

- sd.Choquet.norm
`signature(object = "game")`

`game`

,

`as.card.game-methods`

,

`Choquet.integral-methods`

,

`Mobius-methods`

,

`Sipos.integral-methods`

,

`Sugeno.integral-methods`

,

`pdf.Choquet.unif-methods`

,

`cdf.Choquet.unif-methods`

,

`expect.Choquet.unif-methods`

,

`sd.Choquet.unif-methods`

,

`expect.Choquet.norm-methods`

,

`sd.Choquet.norm-methods`

.

```
## a game (which is a capacity)
mu <- game(c(0,rep(1,15)))
## the attributes of the object
mu@n
mu@data
mu@subsets
## a conversion
as.card.game(mu)
## a transformation
Mobius(mu)
## let us check ...
zeta(Mobius(mu))
## integral calculations
f <- c(0.2,0.3,0.1,0.7)
Choquet.integral(mu,f)
Sugeno.integral(mu,f)
f <- c(0.2,-0.3,0.1,-0.7)
Sipos.integral(mu,f)
```

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