game-class {kappalab}

Class "game"

Description

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

Objects from the Class

Objects can be created by calls to the function game.

Slots

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.

Extends

Class set.func, directly. Class superclass.set.func, by class set.func.

Methods

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")

See Also

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.

Examples

## 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)