Constrained Eigenvalue Minimization of Incomplete Pairwise Comparison Matrices by Nelder-Mead Algorithm

Pairwise comparison matrices play a prominent role in multiple-criteria decision-making, particularly the analytic hierarchy process (AHP). Another form of preference modeling, called an incomplete pairwise matrix, is considered when one or more elements are missing. In this paper, algorithm proposed for optimal completion matrix. Our intention to numerically minimize maximum eigenvalue function, which difficult write explicitly terms variables, subject interval constraints. Numerical simulations carried out order examine performance algorithm. The results our show that has ability solve minimization constrained problem. We provided illustrative examples simplex procedures obtained by algorithm, and how well it fills given matrices.