# entropy-methods: Normalized entropy of a capacity In kappalab: Non-Additive Measure and Integral Manipulation Functions

## 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.

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

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## 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