Two-stage logarithmic goal programming method for generating weights from interval comparison matrices

A two-stage logarithmic goal programming (TLGP) method is proposed to generate weights from interval comparison matrices, which can be either consistent or inconsistent. The first stage is devised to minimize the inconsistency of interval comparison matrices and the second stage is developed to generate priorities under the condition of minimal inconsistency. The weights are assumed to be multiplicative rather than additive. In the case of hierarchical structures, a nonlinear programming method is used to aggregate local interval weights into global interval weights. A simple yet practical preference ranking method is investigated to compare the interval weights of criteria or rank alternatives in a multiplicative aggregation process. The proposed TLGP is also applicable to fuzzy comparison matrices when they are transformed into interval comparison matrices using a-level sets and the extension principle. Six numerical examples including a group decision analysis problem with a group of comparison matrices, a hierarchical decision problem and a fuzzy decision problem using fuzzy comparison matrix are examined to show the applications of the proposed methods. Comparisons with other existing procedures are made whenever possible. (c) 2004 Elsevier B.V. All rights reserved.