Comparing ranking methods: Complete RCI preference and multiplicative preference relations

Abstract

The focus of this paper is comparison of ranking methods. Several methods have been introduced in literature to rank relations and it is noticed that different methods lead to different and possibly contradictory outcomes. To justify why some methods are better than others, a performance parameter needs to be established. We restrict ourselves to the class of Incomplete fuzzy and multiplicative preference relations that can be completed by methods defined by Khalid and Awais (12) and result in additive transitive and Saaty's consistent multiplicative preference relations. For the purpose of ranking, methods are proposed and compared pairwise with the famous fuzzy Borda rule. Also, fuzzy Borda rule for multiplicative preference relations is introduced. To appreciate the most suitable ranking method, we set the performance parameter to be the number of ties produced by each of these methods. So the best rule to rank additive transitive and Saaty's consistent relations is the one producing least number of ties. We prove some useful properties withheld by the considered relations, which helps conclude that these ranking methods are equally efficient for such relations since they produce equal number of ties in the same alternatives. We identify the reason of reaching ties and propose a solution.