Rank aggregation methods dealing with ordinal uncertain preferences

•A two-step rank aggregation model for interval ordinal rankings is proposed.•A matrix retrieving dominance possibilities is built from uncertain data.•Priority vectors are derived from the dominance aggregate matrix.•The model can manage uncertain and incomplete rank information with ties.•Computational methods are proposed to solve the optimization problems. The problem of rank aggregation, also known as group-ranking, arises in many fields such as metasearch engines, information retrieval, recommendation systems and multicriteria decision-making. Given a set of alternatives, the problem is to order the alternatives based on ordinal rankings provided by a group of individual experts. The available information is often limited and uncertain in real-world applications. This paper addresses the general group-ranking problem using interval ordinal data as a flexible way to capture uncertain and incomplete information. We propose a two-stage approach. The first stage learns an aggregate preference matrix as a means of gathering group preferences from uncertain and possibly conflicting information. In the second stage, priority vectors are derived from the aggregate preference matrix based on properties of fuzzy preference relations and graph theory. Our approach provides a theoretical framework for studying the problem that extends some of the methods in the literature, efficient computational methods to solve the problem and some performance measures. It relaxes data certainty and completeness assumptions and overcomes some shortcomings of current group-ranking methods.