capacity-class | R Documentation |
Class representing a capacity, i.e. a monotone set function vanishing at the empty set (also called fuzzy measure, non-additive measure, monotone measure).
Objects can be mainly created by calls
to the functions capacity
and entropy.capa.ident
.
n
:Object of class numeric
of length 1 equal to the
number of elements of the set on which the capacity is defined.
subsets
:Object of class numeric
of length
2^n
containing the power set of the underlying set in
"natural" order. The subsets are coded as integers.
data
:Object of class numeric
of length
2^n
containing the coefficients of the capacity in binary
order. We necessarily have data[1] = 0
plus some additional monotonicity
constraints.
Class game
, directly.
Class superclass.capacity
, directly.
Class set.func
, by class game
.
Class superclass.set.func
, by class game
.
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
signature(object = "capacity")
capacity
,
entropy.capa.ident
,
as.card.capacity-methods
,
conjugate-methods
,
entropy-methods
,
favor-methods
,
is.normalized-methods
,
normalize-methods
,
Mobius-methods
,
orness-methods
,
variance-methods
,
veto-methods
.
## a capacity
mu <- capacity(c(0:13,13,13)/13)
## the attributes of the object
mu@n
mu@data
mu@subsets
## a test
is.normalized(mu)
normalize(mu)
## a conversion that should not work
## as.card.capacity(mu)
## some transformations
conjugate(mu)
Mobius(mu)
## let us check ...
zeta(Mobius(mu))
## some summary indices
orness(mu)
veto(mu)
favor(mu)
variance(mu)
entropy(mu)
## the same
summary(mu)
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