Tropical implementation of the Analytical Hierarchy Process decision method

Understand

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise comparison data.

• In this framework, we first consider the minimax Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale.
• Recasting this approximation problem as a problem of tropical pseudo-quadratic programming we then write out a closed-form solution to it.
• This solution might be either a unique score vector (up to a positive factor) or a set of different score vectors.