Max-algebra and pairwise comparison matrices, II

Nonnegative matrices, max-algebra and applications

Inverse Sensitive Analysis of Pairwise Comparison Matrices

In the analytic hierarchy process (AHP), the consistency of pairwise comparison is measured by the consistency index (CI) value of pairwise comparison matrices. The CI value is defined by the size and the principal eigenvalue of comparison matrix, and the larger the CI value is, the less consistent pairwise comparison is. In this paper, we propose the estimation method of consistency intervals,...

Pairwise comparison matrices: an empirical research

Our research focused on testing various characteristics of pairwise comparison (PC) matrices in controlled experiments. About 270 students have been involved in the test exercises and the final pool contained 450 matrices. Our team conducted experiments with matrices of different size obtained from different types of MADM problems. The matrix elements have been generated by different questionin...

Efficient weight vectors from pairwise comparison matrices

Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and strictly better in at least one position. A weight vector is weakly efficient if the pairwise ratios cannot be improved in all nondiagonal positions. We show t...

Deriving weights from general pairwise comparison matrices

The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matric...