Solving the Least Squares Method problem in the AHP for 3 × 3 and 4 × 4 matrices ⋆

The Analytic Hierarchy Process (AHP) is one of the most pop- ular methods used in Multi-Attribute Decision Making. The Eigenvector Method (EM) and some distance minimizing methods such as the Least Squares Method (LSM) are of the possible tools for computing the prior- ities of the alternatives. A method for generating all the solutions of the LSM problem for 3 × 3 and 4 × 4 matrices is discussed in the paper. Our algorithms are based on the theory of resultants.

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