# is.kadditive-methods: Test method In kappalab: Non-Additive Measure and Integral Manipulation Functions

## Test method

### Description

Tests whether a set function is `k`-additive, i.e., if its M<f6>bius function vanishes for subsets of more than k elements. The set function can be given either under the form of an object of class `set.func`, `card.set.func` or `Mobius.set.func`.

### Details

In order to test whether a coefficient is equal to zero, its absolute value is compared with `epsilon` whose default value is `1e-9`.

### Methods

object = "Mobius.set.func", k = "numeric", epsilon = "numeric", epsilon = "numeric"

Returns an object of class `logical`.

object = "card.set.func", k = "numeric", epsilon = "numeric"

Returns an object of class `logical`.

object = "set.func", k = "numeric", epsilon = "numeric"

Returns an object of class `logical`.

### References

M. Grabisch (1997), k-order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems 92(2), pages 167–189.

M. Grabisch (2000), The interaction and M<f6>bius representations of fuzzy measures on finites spaces, k-additive measures: a survey, in: Fuzzy Measures and Integrals: Theory and Applications, M. Grabisch, T. Murofushi, and M. Sugeno Eds, Physica Verlag, pages 70-93.

`Mobius.set.func-class`,
`card.set.func-class`,
`set.func-class`,
`Mobius-methods`,

`k.truncate.Mobius-methods`.

### Examples

```## a set function
mu <- set.func(c(0,1,1,1,2,2,2,3))
mu