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pord_weakdom {agop}R Documentation

Weak Dominance Relation (Preorder) in the Producer Assessment Problem


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)



numeric vector with nonnegative elements


numeric vector with nonnegative elements


This function only accepts vectors with nonnegative elements.

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


  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).


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.

See Also

Other binary_relations: check_comonotonicity; pord_spread, pord_spreadsym; rel_closure_reflexive, rel_is_reflexive, rel_reduction_reflexive; rel_closure_symmetric, rel_is_symmetric; rel_closure_total_fair, rel_is_total; rel_closure_transitive, rel_is_transitive, rel_reduction_hasse, rel_reduction_transitive; rel_graph; rel_is_antisymmetric; rel_is_asymmetric; rel_is_cyclic; rel_is_irreflexive

Other impact_functions: index.g, index_g, index_g_zi; index.h, index_h; index.lp, index_lp; index.rp, index_rp; index_maxprod; index_w

[Package agop version 0.2-0 Index]