kappalab (version 0.4-0)

Mobius.set.func: Create objects representing the M�bius transform of a set function.

Description

These functions create objects of class Mobius.set.func, Mobius.game, or Mobius.capacity from an object of class numeric.

Usage

Mobius.set.func(object, n, k)
Mobius.game(object, n, k)
Mobius.capacity(object, n, k)
additive.capacity(v)

Arguments

n

An object of class numeric of length 1 equal to the cardinal of the set on which the M�bius{Mobius} representation is defined.

k

An object of class numeric of length 1 equal to the order of truncation of the M�bius{Mobius} representation. Coefficients whose cardinal is superior to k are considered to be zero.

object

Object of class numeric of length choose(n,0) + ... + choose(n,k) representing the coefficients of the truncated M�bius{Mobius} transform in "natural" order.

v

An object of class numeric containing the coefficients of the capacity on singletons.

Value

• Return objects of class Mobius.set.func, Mobius.game, or Mobius.capacity.

See Also

Mobius.capacity-class, Mobius.game-class, Mobius.set.func-class, k.truncate.Mobius-methods.

Examples

Mobius.set.func(c(0,1,1,2,1,2,1,2,2,3,2),4,2)
Mobius.game(c(0,1,1,2,1,2,1,2,2,3,2),4,2)
Mobius.capacity(c(0,1,1,2,1,2,1,2,2,3,2),4,2)
additive.capacity(c(1,2,3,4))