On the extraction of weights from pairwise comparison matrices

A Common Weight Multi-criteria Decision analysis-data Envelopment Analysis Approach with Assurance Region for Weight Derivation from Pairwise Comparison Matrices

Deriving weights from a pairwise comparison matrix (PCM) is a subject for which a wide range of methods have ever been presented. This paper proposes a common weight multi criteria decision analysis-data envelopment analysis (MCDA-DEA) approach with assurance region for weight derivation from a PCM. The proposed model has several merits over the competing approaches and removes the drawbacks of...

Combined Data Envelopment Analysis and Analytical Hierarchy Process Methods to obtain the Favorable Weights from Pairwise Comparison Matrix

A note on deriving weights from pairwise comparison ratio matrices

This paper addresses the Cook and Kress method regarding the use of mathematical programming to derive weights from pairwise comparison ratio matrices. We note that the Cook and Kress formulation has the shortcoming that alternative optimal solutions may occur, which would lead to an infinite set of possible weights. This paper proposes to resolve the problem by formulating a Phase II optimizat...

Deriving weights from general pairwise comparison matrices

The problem of deriving weights from pairwise comparison matrices has been treated extensively in the literature. Most of the results are devoted to the case when the matrix under consideration is reciprocally symmetric (i.e., the i, j-th element of the matrix is reciprocal to its j, i-th element for each i and j). However, there are some applications of the framework when the underlying matric...

Deriving Weights from Pairwise Comparison Matrices: the Additive Case

The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the ar...