Description

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.

Usage

Arguments

Details

We say that a numeric vector x of length n_x is weakly dominated by y of length n_y iff

1. n_x≤ n_y and

2. 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).

Value

Returns a single logical value indicating whether x is weakly dominated by y.

References

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

See Also

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