Consistent Completion of Pairwise Comparison Diagonal Block Matrices

ABSTRACT In this article, we study the problem of how to complete a matrix whose blocks on the main diagonal are reciprocal and known and the blocks outside the main diagonal are unknown. All entries in the main diagonal blocks are known, which means that a partition of the set of alternatives is made and all judgements are made on each subset . First, we study the case when a consistent completion exists and find it. Second, if it is not possible, we find the most consistent completion possible. To this end, we use graph theory.