agop (version 0.1-3)

owa: WAM and OWA Operators

Description

Computes the Weghted Arithmetic Mean or the Ordered Weighted Averaging aggregation operator.

Usage

owa(x, w = rep(1/length(x), length(x)))
  wam(x, w = rep(1/length(x), length(x)))

Arguments

x

numeric vector to be aggregated

w

numeric vector of the same length as x, with elements in $[0,1]$, and such that $\sum_i w_i=1$; weights

Value

• single numeric value

Details

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 greatest 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 of w does not sum up to $1$, then they are normalized and a warning is generated.

Both functions return the ordinary arithmetic mean by default. Special cases of OWA include the trimmed mean (cf. mean) and winsorized mean.

There is a strong connection between the OWA operators and the Choquet integrals.

References

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.

See Also

Other aggregation_operators: owmax, owmin, wmax, wmin