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Relative importance of alternatives in AHP multi-criteria decision problem is standardly computed from the (possibly incosistent) preference matrix as the eigenvector of the preference matrix by methods of linear algebra. Alternative use of non-standard methods in other algebras, such as tropical or fuzzy algebra is considered in this paper. The preference matrix is investigated by the methods used in max-prod algebra. Given preference matrix is processed by max-prod operations, until a steady state is reached. The eigenvector of the matrix then describes the steady state preferences and respects all preference relations contained in the original matrix. Efficient algorithms for computing eigenvectors in the tropical algebra are described. The method is illustrated by numerical examples and compared with the linear algebra approach. The consistent and inconsistent cases are considered.

Preference Matrices in Tropical Algebra