Fundamentals of the analytic network process — multiple networks with benefits,costs, opportunities and risks

The general theory of the ANP enables one to deal with the benefits, opportunities, costs, and risks (the BOCR merits) of a decision, by introducing the notion of negative priorities for C and R along with the rating (not comparison) of the top priority alternative synthesized for each of the four merits in terms of strategic criteria to enable one to combine the four B, O, C, and R values of each alternative into a single outcome. Strategic criteria are very basic criteria individuals and groups use to assess whether they should make any of the many decisions they face in their daily operations. They do not depend on any particular decision for their priorities but are assessed in terms of the goals and values of the individual or organization. Synthesis is made with two formulas, one multiplicative and one additive subtractive that can give rise to negative overall priorities. This paper summarizes and illustrates basic complex decisions involving several control criteria under each of the BOCR merits. Thomas L. Saaty holds the Chair of University Professor, Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA, and obtained his Ph.D. in mathematics from Yale University. Before that he was a professor at the Wharton School of the University of Pennsylvania for ten years. Prior to that he spent seven years at the Arms Control and Disarmament Agency in the State Department in Washington, DC, that carried out the arms reduction negotiations with the Soviets in Geneva. His current research interests include decision-making, planning, conflict resolution and synthesis in the brain. As a result of his search for an effective means to deal with weapons tradeoffs at the Disarmament Agency and, more generally, with decision-making and resource allocation, Professor Saaty developed The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP). He is co-developer of the software Expert Choice and of the software Super Decisions for decisions with dependence and feedback. He has authored or co-authored twelve books on the AHP/ANP. Professor Saaty has also written a number of other books that embrace a variety of topics, including Modern Nonlinear Equations, Nonlinear Mathematics, Graph Theory, The Four Color Problem, Behavioral Mathematics, Queuing Theory, Optimization in Integers, Embracing the Future and The Brain: Unraveling the Mystery of How It Works. His most recent book is Creative Thinking, Problem Solving & Decision Making. 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. He has published more than 300 referred articles in a wide variety of professional journals. He has been on the editorial boards of Mathematical Reviews, Operations Research, Naval Research Logistics Quarterly, Mathematical and Computer Modeling, Socio-Economic Planning Sciences, Applied Mathematics Letters, and several others. He also served as consultant to many corporations and government.     

FUNDAMENTALS OF THE ANALYTIC NETWORK PROCESS- DEPENDENCE AND FEEDBACK IN DECISION-MAKING WITH A SINGLE NETWORK

The Analytic Network Process (ANP) is a multicriteria theory of measurement used to derive relative priority scales of absolute numbers from individual judgments (or from actual measurements normalized to a relative form) that also belong to a fundamental scale of absolute numbers. These judgments represent the relative influence, of one of two elements over the other in a pairwise comparison process on a third element in the system, with respect to an underlying control criterion. Through its supermatrix, whose entries are themselves matrices of column priorities, the ANP synthesizes the outcome of dependence and feedback within and between clusters of elements. The Analytic Hierarchy Process (AHP) with its independence assumptions on upper levels from lower levels and the independence of the elements in a level is a special case of the ANP. The ANP is an essential tool for articulating our understanding of a decision problem. One had to overcome the limitation of linear hierarchic structures and their