Characterization of the Optimal Bucket Order Problem Instances and Algorithms by Using Fuzzy Logic

The problem of aggregating several rankings in order to obtain a consensus ranking that generalizes them is an active field of research with several applications. The Optimal Bucket Order Problem (OBOP) is a rank aggregation problem where the resulting ranking may be partial, i.e. ties are allowed. Several algorithms have been proposed for OBOP. However, their performances with respect to the characteristics of the instances are not studied properly. This paper uses fuzzy logic in order to describe different aspects of OBOP instances (such as the number of items to be ranked, distribution of the precedences values, and the utopicity) and the performance of several OBOP algorithms. Based on this fuzzy characterization, several fuzzy relations between instance characteristics and the performance of the algorithms have been discovered.