pord_weakdom {agop} | R Documentation |
Checks whether a given numeric vector of arbitrary length is (weakly) dominated by another vector, possibly of different length, in terms of (sorted) elements' values and their number.
pord_weakdom(x, y)
x |
numeric vector with nonnegative elements |
y |
numeric vector with nonnegative elements |
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 it holds x_{(n_x-i+1)}≤ y_{(n_y-i+1)}.
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.
Note that this dominance relation gives the same value for all permutations of input vectors' element. Such a preorder is tightly related to symmetric impact functions: each impact function is a morphism between weak-dominance-preordered set of vectors and the set of reals equipped with standard linear ordering (see Gagolewski, Grzegorzewski, 2011 and Gagolewski, 2013).
Returns a single logical value
indicating whether x
is weakly
dominated by y
.
Gagolewski M., Grzegorzewski P., Possibilistic Analysis of Arity-Monotonic Aggregation Operators and Its Relation to Bibliometric Impact Assessment of Individuals, International Journal of Approximate Reasoning 52(9), 2011, pp. 1312-1324.
Gagolewski M., Scientific Impact Assessment Cannot be Fair, Journal of Informetrics 7(4), 2013, pp. 792-802.
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_nd
, pord_spread
,
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
Other impact_functions: index_g
,
index_h
, index_lp
,
index_maxprod
, index_rp
,
index_w