Efficient vectors for simple perturbed consistent matrices

Henrique F. da Cruz

doi:10.1016/j.ijar.2021.09.007

Efficient vectors for simple perturbed consistent matrices

2021-12-01

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AI

DOI：10.1016/j.ijar.2021.09.007

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Abstract

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In the Analytic Hierarchy process, a method used in Decision Making, it may be important to approximate a pairwise comparison matrix (PC matrix) by a consistent one. In this context, the notion of efficient vector for a PC matrix arises. In this paper we describe all efficient vectors for an n x n comparison pairwise matrix obtained from a consistent one by perturbing one entry above the main diagonal, and the corresponding reciprocal entry. As a consequence, we give a simple proof of the result obtained by K. Abele-Nagy and S. Bozoki (2016) that states that the principal eigenvector of a simple perturbed consistent matrix is efficient. In addition, we consider a set of non-efficient vectors associated with the simple perturbed consistent matrix and describe all the efficient vectors that dominate each vector in that set. (C) 2021 Elsevier Inc. All rights reserved.

Keywords:

Decision-making

Consistent matrix

Pairwise comparison matrix

Vector efficiency

Efficient vectors for simple perturbed consistent matrices

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