d2owa_checkwts {agop} | R Documentation |
Computes the D2OWA operator, i.e., the normalized L2 distance between a numeric vector and an OWA operator.
d2owa_checkwts(w) d2owa(x, w = rep(1/length(x), length(x)))
w |
numeric vector of the same length as |
x |
numeric vector to be aggregated |
D2OWA is a symmetric spread measure.
It is defined as
d2owa(x) == sqrt(mean((x-owa(x,w))^2))
.
Not all weights, however, generate a proper function of this kind;
d2owa_checkwts
may be used to check that.
For d2owa
, if w
is not appropriate, an error is thrown.
w
is automatically normalized so that its elements sum up to 1.
For d2owa
, a single numeric value is returned.
On the other hand, d2owa_checkwts
returns a single logical value.
Gagolewski M., Spread measures and their relation to aggregation functions, European Journal of Operational Research 241(2), 2015, pp. 469-477. doi:10.1016/j.ejor.2014.08.034
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.