Comparing apples and oranges: the weighted OWA function

This paper advocates the use of weighted ordered weighted averaging (WOWA) functions in decision-making processes, where the alternatives are not directly comparable. In particular, WOWA allows one to compare the strongest points of each alternative, also weighted by the importance of each criterion. Four different approaches to applying weights in OWA functions are reviewed. Torra's method based on interpolating regular increasing monotone quantifier and the pruned n-ary tree are compared to the WOWA obtained from recently proposed implicit averaging. Computationally efficient algorithms are outlined. The use of WOWA is illustrated in several examples.