kappalab (version 0.4-0)

is.kadditive-methods: Test method

Description

Tests whether a set function is k-additive, i.e., if its M�bius{Mobius} 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.

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�bius{Mobius} 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.

See Also

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
is.kadditive(mu,2)
is.kadditive(mu,1)

## the M�bius representation of a set function, 2-additive by construction 
a <- Mobius.set.func(c(0,1,2,1,3,1,2,1,2,3,1),4,2)
is.kadditive(a,2)
is.kadditive(a,1)