Java implementations for WOWA, OWA and weighted means (WM)
The file
ww.tar.gz
(source code in
wwPublic.tar.gz )
contains a Java implementation of WM (Weighted Mean), OWA and WOWA operators.
The WOWA (Weighted Ordered Weighted Aggregation) operator was introduced in:
V. Torra, The Weighted OWA operator,
Int. J. of Intel. Systems, 12 (1997) 153-166.
Paper at Wiley
The implementation given here uses the interpolation method described in:
V. Torra, The WOWA operator and the interpolation function W*:
Chen and Otto's interpolation method revisited,
Fuzzy Sets and Systems, 113:3 (2000) 389-396.
Paper Sciencedirect
A discussion of different interpolation methods is given in
V. Torra, Z. Lv, On the WOWA operator and its interpolation function. Int. J. Intell. Syst. 2:(1 (2009): 1039-105
Paper at Wiley
A review on the WOWA
V. Torra, The WOWA Operator: A Review, in R. R. Yager, J. Kacprzyk, G. Beliakov (eds.) Recent Developments in the Ordered Weighted Averaging Operators, Springer 2011 17-28.
Paper at Springer
Implementation of the wowa operator is given in the folder ww.
An example file to use the operators is given in the root: testWowa.java
The WOWA operator:
The WOWA operator is an aggregation function that generalizes the weighted mean and the OWA operator (Yager, 1988). By means of considering two different weighting vectors, the WOWA operator allows the fusion of a given set of numerical values considering both the importance of the sources that have supplied the values (as in the weighted mean) and the degree of compensation or tradeoff between large and small values (as in the OWA operator).
From a formal point of view, the WOWA operator is a particular case of Choquet integral (using a particular type of measure: a distorted probability).