Interactive procedure for non-transitivity revealing and correcting under pairwise comparisons

The paper considers the problem of revealing and correcting non-transitivity in DM’s preferences (if the assumption about the transitivity of binary relation is valid). The binary relation is represented as a digraph whose vertices correspond to the objects of the initial set. After the DM’s answer the corresponding arc is added to graph if and only if its addition does not form cycles in graph. The revealing of the cylces is carried out through the search cycles in graph. The revealing of the cycles is carried out through the search for paths between the vertices in direction opposite to the last reply. The presence of such paths shows that the last DM’s answer contradicts his previous answers (violation of transitivity). If DM insists on the last answer the paths between the corresponding pair of objects are displayed in succession to DM, beginning from the shortest paths, for analysis and correction of contradictions. After breaking all cycles the arc corresponding to the last answer may be added in graph. If it is not possible to break all of the cycles the assumption about transitivity is considered as invalid.