The Myth of the Importance of Consistency in Analytical Hierarchical Processes

In this work, rather than relating different areas of knowledge, the authors make use of logic, which is intrinsic to mathematical models. They discuss one of the fallacies that hides behind the analytic hierarchy process (AHP). In particular, the analysis of the consistency index, sometimes referred as the Saaty consistency or simply the consistency, will be discussed. The AHP is based on three fundamental axioms: reciprocity, homogeneity, and synthesis. However, it gives a great relevance to consistency, which is managed like a fourth axiom. On each of these four axioms, some comments will be made. However, this work will focus mainly on discussing the importance of the consistency index, to which, undoubtedly, a large number of essays and many hours of work have been devoted. In trying to answer the question, the calculation of consistency is really important. The aim of the paper is to raise a discussion of one of the fallacies that hides behind the analytic hierarchy process and present a simple and direct way to handle Saaty consistency.