entropy-methods: Normalized entropy of a capacity

In kappalab: Non-Additive Measure and Integral Manipulation Functions

Normalized entropy of a capacity

Description

Computes the normalized entropy of a capacity. The capacity can be given either under the form of an object of class capacity, card.capacity or Mobius.capacity.

Methods

object = "Mobius.capacity"

The normalized entropy is computed from the Möbius transform of a capacity.

object = "capacity"

The normalized entropy is computed directly from a capacity.

object = "card.capacity"

The normalized entropy is computed from a cardinal capacity.

References

J-L. Marichal (2002), Entropy of discrete Choquet capacities, European Journal of Operational Research, 3:137, 2002, pages 612-624.

I. Kojadinovic, J-L. Marichal and M. Roubens (2005), An axiomatic approach to the definition of the entropy of a discrete Choquet capacity, Information Sciences 172, pages 131-153.

See Also

capacity-class,
Mobius.capacity-class,
card.capacity-class,
Mobius-methods.

Examples

## a capacity
mu <- capacity(c(0,0,0:13))

## its Mobius transform
a <- Mobius(mu)

## their normalized entropy
entropy(mu)
entropy(a)

## similar examples with card.capacity objects
mu <- lower.capacity(4)
entropy(mu)
mu <- uniform.capacity(4)
entropy(mu)

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