owa {agop} | R Documentation |
Computes the Weighted Arithmetic Mean or the Ordered Weighted Averaging aggregation operator.
owa(x, w = rep(1/length(x), length(x)))
wam(x, w = rep(1/length(x), length(x)))
x |
numeric vector to be aggregated |
w |
numeric vector of the same length as |
The OWA operator is given by
\mathsf{OWA}_\mathtt{w}(\mathtt{x})=\sum_{i=1}^{n} w_{i}\,x_{(i)}
where x_{(i)}
denotes the i
-th smallest
value in x
.
The WAM operator is given by
\mathsf{WAM}_\mathtt{w}(\mathtt{x})=\sum_{i=1}^{n} w_{i}\,x_{i}
If the elements in w
do not sum up to 1
, then
they are normalized and a warning is generated.
Both functions by default return the ordinary arithmetic mean.
Special cases of OWA include the trimmed mean (see mean
)
and Winsorized mean.
There is a strong, well-known connection between the OWA operators and the Choquet integrals.
These functions return a single numeric value.
Choquet G., Theory of capacities, Annales de l'institut Fourier 5, 1954, pp. 131-295.
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
Yager R.R., On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man, and Cybernetics 18(1), 1988, pp. 183-190.
Other aggregation_operators:
owmax()