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)))
For d2owa, a single numeric value is returned.
On the other hand, d2owa_checkwts returns a single logical value.
numeric vector of the same length as x, with elements in \([0,1]\),
and such that \(\sum_i w_i=1\); weights
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.
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.