2 research outputs found
On the geometric mean method for incomplete pairwise comparisons
When creating the ranking based on the pairwise comparisons very often, we
face difficulties in completing all the results of direct comparisons. In this
case, the solution is to use the ranking method based on the incomplete PC
matrix. The article presents the extension of the well known geometric mean
method for incomplete PC matrices. The description of the methods is
accompanied by theoretical considerations showing the existence of the solution
and the optimality of the proposed approach.Comment: 15 page
A general unified framework for interval pairwise comparison matrices
Interval Pairwise Comparison Matrices has been widely used to account for uncertain statements concerning the preferences of decision makers. Several approaches have been proposed in the literature, such as multiplicative and fuzzy interval matrices. In this paper, we propose a general unified approach to Interval Pairwise Comparison Matrices, based on Abelian linearly ordered groups. In this framework, we generalize some consistency conditions provided for multiplicative and/or fuzzy interval pairwise comparison matrices and provide inclusion relations between them. Then, we provide a concept of distance between intervals that, together with a notion of mean defined over real continuous Abelian linearly ordered groups, allows us to provide a consistency index and an indeterminacy index. In this way, by means of suitable isomorphisms between Abelian linearly ordered groups, we will be able to compare the inconsistency and the indeterminacy of different kinds of Interval Pairwise Comparison Matrices, e.g. multiplicative, additive, and fuzzy, on a unique Cartesian coordinate system