Weighted and logarithmic least square methods for mutual evaluation network system including AHP and ANP

In this paper we show that the weighted least square (WLS) and the logarithmic least square (LLS) of various methods to solve the mutual evaluation network (MEN) system including the Analytic Hierarchy Process (AHP) and the Analytic Network Process (ANP), are superior to others. Both methods can solve MEN problems without any restrictions of the structure matrix of MEN. We also show that the WLS always gives positive solutions, which generalize the proof by Blankmeyer. We establish the error analysis of WLS and LLS. Especially, we give solving methods of MEN problems with different variances of errors by the WLS and the LLS.