pord_nd {agop} | R Documentation |
Checks whether a numeric vector of arbitrary length is (weakly) dominated (elementwise) by another vector of the same length.
pord_nd(x, y, incompatible_lengths = NA)
x |
numeric vector with nonnegative elements |
y |
numeric vector with nonnegative elements |
incompatible_lengths |
single logical value,
value to return iff lengths of |
We say that a numeric vector x
of length n_x
is weakly dominated by y
of length n_y
iff
n_x=n_y
and
for all i=1,\dots,n_x
it holds
x_i\le y_i
.
This relation is a preorder: it is reflexive (see rel_is_reflexive
)
and transitive (see rel_is_transitive
),
but not necessarily total (see rel_is_total
).
See rel_graph
for a convenient function
to calculate the relationship between all pairs of elements
of a given set.
Such a preorder is tightly related to classical aggregation functions: each aggregation function is a morphism between weak-dominance-preordered set of vectors and the set of reals equipped with standard linear ordering.
Returns a single logical value
indicating whether x
is weakly
dominated by y
.
Grabisch M., Marichal J.-L., Mesiar R., Pap E., Aggregation functions, Cambridge University Press, 2009.
Gagolewski M., Data Fusion: Theory, Methods, and Applications, Institute of Computer Science, Polish Academy of Sciences, 2015, 290 pp. isbn:978-83-63159-20-7
Other binary_relations:
check_comonotonicity()
,
pord_spread()
,
pord_weakdom()
,
rel_graph()
,
rel_is_antisymmetric()
,
rel_is_asymmetric()
,
rel_is_cyclic()
,
rel_is_irreflexive()
,
rel_is_reflexive()
,
rel_is_symmetric()
,
rel_is_total()
,
rel_is_transitive()
,
rel_reduction_hasse()