d2owa_checkwts {agop}R Documentation

D2OWA Operators

Description

Computes the D2OWA operator, i.e., the normalized L2 distance between a numeric vector and an OWA operator.

Usage

d2owa_checkwts(w)

d2owa(x, w = rep(1/length(x), length(x)))

Arguments

w

numeric vector of the same length as x, with elements in [0,1], and such that sum(x)=1; weights

x

numeric vector to be aggregated

Details

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.

Value

For d2owa, a single numeric value is returned. On the other hand, d2owa_checkwts returns a single logical value.

References

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.


[Package agop version 0.2-3 Index]