Super Pairwise Comparison Matrix with the Logarithmic Least-Squares Method

We have proposed a super pairwise comparison matrix (SPCM) to express all pairwise comparisons in the evaluation process of the dominant analytic hierarchy process (AHP) or the multiple dominant AHP (MDAHP) as a single pairwise comparison matrix. This paper shows, using the error models, that in the dominant AHP an evaluation value resulting from the application of the logarithmic least-squares method (LLSM) to a SPCM necessarily coincide with that of the evaluation value resulting obtained by using the geometric mean method to each pairwise comparison matrix. This paper also shows, using the error models, that in MDAHP an evaluation value resulting from the application of the logarithmic least-squares method (LLSM) to a SPCM does not necessarily coincide with that of the evaluation value resulting from the application of the geometric mean multiple dominant AHP (GMMDAHP) to the evaluation value obtained from each pairwise comparison matrix by using the geometric mean method.