Mobius.game-class: Class "Mobius.game"

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Class "Mobius.game"

Description

Class representing the Möbius transform of a game.

Objects from the Class

Objects can be created by calls to the function Mobius.game.

Slots

n:

Object of class numeric of length 1 containing the number of elements of the set on which the Möbius transform is defined.

k:

Object of class numeric of length 1 containg the order of truncation of the Möbius transform: subsets whose cardinal is superior to k are considered to be zero.

subsets:

Object of class numeric containing the "k power set" of the underlying set in "natural" order . The subsets are encoded as integers.

data:

Object of class numeric of length choose(n,0) + ... + choose(n,k) representing the coefficients of a truncated Möbius transform of a game in "natural" order.

Extends

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

Methods

Choquet.integral

signature(object = "Mobius.game", f = "numeric")

Sipos.integral

signature(object = "Mobius.game", f = "numeric")

Sugeno.integral

signature(object = "Mobius.game", f = "numeric")

zeta

signature(object = "Mobius.game")

See Also

game-class,
Mobius.game,
Choquet.integral-methods,
Sipos.integral-methods,
Sugeno.integral-methods,
zeta-methods,
expect.Choquet.norm-methods.

Examples

## a game (which is a capacity)
mu <- game(c(0,rep(1,15)))
## and its Mobius representation
a <- Mobius(mu)

# the attributes of object a
a@n
a@k
a@data
a@subsets

## a transformation
zeta(a)
## let us check ...
Mobius(zeta(a))

## integral calculations 
f <- c(0.2,0.3,0.1,0.7)
Choquet.integral(a,f)
Sugeno.integral(a,f)
f <- c(0.2,-0.3,0.1,-0.7)
Sipos.integral(a,f)

kappalab documentation built on Nov. 8, 2023, 1:07 a.m.