is.kadditive-methods | R Documentation |
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
.
In order to test whether a coefficient is equal to zero, its
absolute value is compared with epsilon
whose default
value is 1e-9
.
Returns an object of class logical
.
Returns an object of class logical
.
Returns an object of class logical
.
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
.
## 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 Mobius 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)
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