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DECISION MAKING – THE ANALYTIC HIERARCHY AND
NETWORK PROCESSES (AHP/ANP)
Thomas L. SAATY
University of Pittsburgh
saaty@
Abstract
This is the first part of an introduction to multicriteria decision making using the Analytic
Hierarchy Process (AHP) and its generalization, the Analytic Network Process (ANP). The discussion
involves individual and group decisions both with the independence of the criteria from the
alternatives as in the AHP and also with dependence and feedback in the entire decision structure as in
the ANP. This part explains the Analytic Hierarchy Process, with examples, and presents in some
detail the mathematical foundations. An exposition of the Analytic Network Process and its
applications will appear in later issues of this journal.
Keywords: Decision making, Analytic Hierarchy Process (AHP), Analytic Network Process (ANP)
1. Introduction
(Saaty 1977, 1994,
2000a, 2000b and 2001)
Decision making involves criteria and
alternatives to choose from. The criteria
usually have different importance and the
alternatives in turn differ in our preference for
them on each criterion. To make such tradeoffs
and choices we need a way to measure.
Measuring needs a good understanding of
methods of measurement and different scales
of measurement.
Many people think that measurement needs
a physical scale with a zero and a unit to apply
to objects or phenomena. That is not true.
Surprisingly enough, we can also derive
accurate and reliable relative scales that do not
have a zero or a unit by using our
understanding and judgments that are, after all,
the most fundamental determinants of why we
want to measure something. In reality we do
that all the time and we do it subconsciously
without thinking about it. Physical scales help
our understanding and use of the things that we
know how to measure. After we obtain
readings from a physical scale, they still need
to be interpreted according to what they mean
and how adequate or inadequate they are to
satisfy some need we have. But the number of
things we don’t know how to measure is
infinitely larger than the things we know how
to measure, and it is highly unlikely that we
will ever find ways to measure everything on a
physical scale with a unit. Scales of
measurement are inventions of a technological
mind. Our minds and ways of understanding
we have had with us and will always have. The
brain is an electrical device of neurons whose
ISSN 1004-3756/04/1301/1
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Decision Making – The Analytic Hierarchy and Network Processes (AHP/ANP)
firings and synthesis must perform
measurement with great accuracy to give us all
the meaning and understanding that we have to
enable us to survive and reach out to control a
complex world. Can we rely on our minds to
be accurate guides with their judgments? The
answer depends on how well we know the
phenomena to which we apply measurement
and how good our judgments are to represent
our understanding. In our own personal affairs
we are the best judges of what may be good for
us. In situations involving many people, we
need the judgments from all the participants. In
general we think that there are people who are
more expert than others in some areas and their
judgments should have precedence over the
judgments of those who know less as in fact is
often the case in practice.
Judgments expressed in the form of
comparisons are fundamental in our biological
makeup. They are intrinsic in the operations of
our brains and that of animals and one might
even say of plants since, for example, they
control how much sunlight to admit. We all
make decisions every moment, consciously or
unconsciously, today and tomorrow, now and
forever, it seems. Decision-making is a
fundamental process that is integral in
everything we do. How do we do it? The
Harvard psychologist Arthur Blumenthal tells
us in his book The Process of Cognition,
Prentice-Hall, Inc., Englewood Cliffs, New
Jersey, 1977, that there are two types of
judgment: “Comparative judgment which is
the identification of some relation between two
stimuli both present to the observer, and
absolute judgment which involves the relation
between a single stimulus and some
information held in short term memory about
some former comparison stimuli or about some
previously experienced measurement scale
using which the observer rates the single
stimulus.”
When we think about it, both these
processes involve making comparisons.
Comparisons imply that all things we know are
understood in relative terms to other things. It
does not seem possible to know an absolute in
itself independently of something else that
influences it or that it influences. The question
then is how do we make comparisons in a
scientific way and derive from these
comparisons scales of relative measurement?
When we have many scales with respect to a
diversity of criteria and subcriteria, how do we
synthesize these scales to obtain an overall
relative scale? Can we validate this process so
that we can trust its reliability? What can we
say about other ways people have proposed to
deal with judgment and measurement, how do
they relate to this fundamental idea of
comparisons, and can they be relied on for
validity? These are all questions we need to
consider in making a decision. It is useful to
remember that there are many people in the
world who only know their feelings and may
know nothing about numbers and never heard
of them but can still make good decisions, how
do they do it? It is unlikely that by guessing at
numbers and assigning them directly to the
alternatives to indicate order under a criterion
will yield meaningful priorities because the
numbers are arbitrary. Even if they are taken
from a scale for a particular criterion, how
would we combine them across the criteria as
they would likely be from different scales? Our
answer to this conundrum is to derive a relative
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