Abstract:

The existence of a best approximation to the pairwise comparison matrix from the set of consistent matrices is proved. At the same time, we can also prove that there are many best approximations. The transformation from the original non-linear approximation into a linear one by using diffeomorphism is proposed. Finally a method of best approximation is obtained, and a simple example is given.

Key words: analytic hierarchy process, best approximation, pai-rwise comparison matrix, consistent matrix, diffeomorphism, projection theorem