Fuzzy ranking from fuzzy pairwise comparisons with applications

Abstract

One method of ranking items is to score all of them against a standard scale. Sometimes it is difficult to create or use such a scale. As an alternative, it is possible to make side-by-side comparisons of some or all of the pairs of items. Then the problem is to convert the collective pairwise comparisons into a ranking. This problem has been studied previously in many contexts. This thesis addresses several methods, including where fuzzy comparisons are made for some, but not all, of the pairs. The Colley method and PageRank algorithm both use pairwise comparisons for some pairs to rank all items in a set. This thesis shows how those pairwise comparisons can be fuzzy. It also shows how Saaty's method for ranking alternatives can be completed when not all comparisons are used.