kappalab (version 0.4-7)

k.truncate.Mobius-methods: k-order truncation of the Mbius representation of a set function.

Description

Truncates the Mbius representation of a set function by considering that the values of subsets whose cardinal is superior to k are zero. The result is at most k-additive.

Methods

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

Returns an object of class Mobius.set.func. The Mbius representation of the set function is first computed and then k-truncated.

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

Returns an object of class Mobius.set.func.

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 Mbius 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, set.func-class, Mobius-methods.

Examples

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

## 2-truncate it
k.truncate.Mobius(mu,2)
## 2-truncate it
k.truncate.Mobius(Mobius(mu),2)