Characterization of the consistent completion of analytic hierarchy process comparison matrices using graph theory

Antonella Certa, Silvia Carpitella, Silvia Carpitella, Joaquín Izquierdo, Julio Benítez

Risultato della ricerca: Articlepeer review

9 Citazioni (Scopus)


Decision-making is frequently affected by uncertainty and/or incomplete information, which turn decision-making into a complex task. It is often the case that some of the actors involved in decision-making are not sufficiently familiar with all of the issues to make the appropriate decisions. In this paper, we are concerned about missing information. Specifically, we deal with the problem of consistently completing an analytic hierarchy process comparison matrix and make use of graph theory to characterize such a completion. The characterization includes the degree of freedom of the set of solutions and a linear manifold and, in particular, characterizes the uniqueness of the solution, a result already known in the literature, for which we provide a completely independent proof. Additionally, in the case of nonuniqueness, we reduce the problem to the solution of nonsingular linear systems. In addition to obtaining the priority vector, our investigation also focuses on building the complete pairwise comparison matrix, a crucial step in the necessary process (between synthetic consistency and personal judgement) with the experts. The performance of the obtained results is confirmed.
Lingua originaleEnglish
pagine (da-a)3-15
Numero di pagine13
RivistaJournal of Multi-Criteria Decision Analysis
Stato di pubblicazionePublished - 2019

All Science Journal Classification (ASJC) codes

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  • ???subjectarea.asjc.1400.1408???


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