Mobius.gen: Create objects representing the Möbius transform of a set...

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Create objects representing the Möbius 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 Möbius representation is defined.
k	An object of class numeric of length 1 equal to the order of truncation of the Möbius 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 Möbius 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))

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