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decision making in complex environment
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DECISION MAKING IN
COMPLEX ENVIRONMENTS
The Analytic Hierarchy Process (AHP)
for Decision Making
and
The Analytic Network Process (ANP)
for Decision Making with
Dependence and Feedback
Rozann W. Saaty
Software for Decision Making with Dependence and Feedback
SUPER DECISIONS
i
Copyrights and Acknowledgments
This material was assembled from works by Thomas L. Saaty and from student projects in his
classes done over several years. The instructions on how to use the SuperDecisions software
were prepared by Rozann W. Saaty of the Creative Decisions Foundation. The software that
implements the Analytic Network Process, SuperDecisions, was developed by William J.
Adams of Embry Riddle Aeronautical University, Daytona Beach, Florida, working with Rozann
W. Saaty.
© Rozann W. Saaty February 2003
This material may not be reproduced in any form without the permission of Rozann W. Saaty or
Thomas L. Saaty.
Rozann W. Saaty
Creative Decisions Foundation
4922 Ellsworth Avenue
Pittsburgh, PA 15213
Phone: 412-621-6546
e-mail: rozann@creativedecisions.net
Thomas L. Saaty
322 Mervis Hall
Katz Graduate School of Business
University of Pittsburgh
Pittsburgh, PA 15260
Phone: 412-648-1539
e-mail: saaty@katz.pitt.edu
ii
Biography
Thomas Saaty holds the Chair of University Professor at the University of Pittsburgh. He
received his Ph.D. in mathematics with a minor in physics from Yale University. From 1963-
1969, he worked at the Arms Control and Disarmament Agency in Washington. From 1969-
1979, he was a professor at the Wharton School of the University of Pennsylvania where he
developed the Analytic Hierarchy Process for decision-making. Inspired by world events that
took place during his time at the Arms
Control agency, the AHP was his answer
for how to deal with weapons tradeoffs,
resource allocation and decision-making.
He has written eight books devoted to the
theory and applications of the Analytic
Hierarchy Process (AHP) and its
generalization, the Analytic Network
Process (ANP) for decision making with
dependence and feedback. He has also
written books on Modern Nonlinear
Equations, Nonlinear Mathematics,
Graph Theory, The Four Color Problem,
Behavioral Mathematics, Queuing
Theory, Optimization in Integers, and
Embracing the Future, as well as
numerous papers. He has also served as a
consultant to many corporations and
governments. His research interests
include decision-making, planning, and
the analysis of neural functions. His most
recent book, published in 2001, is
Creative Thinking, Problem Solving &
Decision Making. It includes a
powerpoint slide presentation on a CD.
The book is a rich collection of ideas,
incorporating research by a growing body
of researchers and practitioners, profiles
of creative people, projects and products,
theory, philosophy, physics and metaphysics…all explained with a liberal dose of humor. Dr.
Saaty is the co-developer of AHP and ANP software and of the ANP software SuperDecisions
for decision-making with dependence and feedback.
iii
FOREWORD
We want this book to help people be exemplary survivors, persistent and durable, creative
decision-makers and leaders, effective negotiators, doers and implementers of ideas and plans.
The Analytic Network Process (ANP) is the most comprehensive framework for the analysis of
societal, governmental and corporate decisions that is available today to the decision-maker. It
allows one to include all the factors and criteria, tangible and intangible that have bearing on
making a best decision. The Analytic Network Process allows both interaction and feedback
within clusters of elements (inner dependence) and between clusters (outer dependence). Such
feedback best captures the complex effects of interplay in human society, especially when risk
and uncertainty are involved.
The ANP, developed by Thomas L. Saaty, provides a way to input judgments and measurements
to derive ratio scale priorities for the distribution of influence among the factors and groups of
factors in the decision. Ratio scales make possible proportionate allocation of resources
according to derived priorities. The well-known decision theory, the Analytic Hierarchy Process
(AHP) is a special case of the ANP. Both the AHP and the ANP derive ratio scale priorities by
making paired comparisons of elements on a common property or criterion. Although many
decision problems are best studied through the ANP, one may wish to compare the results
obtained with it to those obtained using the AHP or any other decision approach with respect to
the time it took to obtain the results, the effort involved in making the judgments, and the
relevance and accuracy of the results.
ANP models have three parts: the first is a strategic criteria in terms of which a decision is
evaluated according to its merits of Benefits, Opportunities, Costs and Risk. Each merit provides
control criteria for the second part of the decision and with each control criterion there is
associated a network of influences that determine the priorities of the alternatives of the decision
for that control criterion. The priorities of the merits and those of the control criteria are then
used to synthesize the priorities of the alternatives to obtain the final best answer. The
supermatrix and its powers are the fundamental tools needed to lay out the workings of the ANP
The ANP has been applied to a large variety of decisions: marketing, medical, political, military,
social, forecasting and prediction and many others. Its accuracy of prediction is impressive in
applications that have been made to economic trends, sports and other events for which the
outcome later became known. Detailed case studies of applications are included in this book and
also in the book, The Analytic Network Process: Decision Making with Dependence and
Feedback, by Thomas L. Saaty.
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