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The AHP/ANP are multicriteria decision-making theories that deal with bothhierarchic structures when the criteria are independent of the alternatives andwith networks when there is any dependence within and between elements of thedecision. Both of them have been repeatedly used in practice by variousresearchers and practitioners. From the perspective of almost 40 years ofpractice in solving problems using both theories, some of their properties seemto be more important than others. The article indicates four of them asfundamental for understanding AHP/ANP. These are the axioms related tostructure, computation, and expectation. The mathematical formulation of theaxioms is preceded by an introduction explaining the motivation behind theintroduced concepts. The article is expository and it is an improved andrefined version of the work [1].

Axioms of the Analytic Hierarchy Process (AHP) and its Generalization to Dependence and Feedback: The Analytic Network Process (ANP)