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