Non-uniqueness of Interval Weight Vector to Consistent Interval Pairwise Comparison Matrix and Logarithmic Estimation Methods

In this paper we investigate the interval priority weight estimation from a given interval pairwise comparison matrix. The lower and upper models as well as goal programming model were proposed. It has been expected that the sum of widths of interval weights estimated by lower model is not greater than that estimated by upper model. We show that this expectation is not always hold. Especially when the given interval comparison matrix is totally consistent, it is possible that the solution is not unique and the reverse inequality relation holds. We investigate uniqueness conditions of interval comparison matrices and the influence of non-uniqueness in the comparison of alternatives. Based on the results of investigation above, we propose interval weight estimation methods from interval pairwise comparison matrix.