entropy-methods: Normalized entropy of a capacity

Description Methods References See Also Examples

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 M<f6>bius 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

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## 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)

Example output

Loading required package: lpSolve
Loading required package: quadprog
Loading required package: kernlab
[1] 0.8073944
[1] 0.8073944
[1] 0
[1] 1

kappalab documentation built on May 2, 2019, 5:49 a.m.