Weak Dominance Relation (Preorder)
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,…,n_x it holds x_i≤ 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
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