pord_weakdom {agop} | R Documentation |
Weak Dominance Relation (Preorder) in the Producer Assessment Problem
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
pord_weakdom(x, y)
Arguments
x |
numeric vector with nonnegative elements |
y |
numeric vector with nonnegative elements |
Details
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
- 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).
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.
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