Showing papers by "Thomas L. Saaty published in 2001"

Fundamentals of the Analytic Hierarchy Process

Abstract: The seven pillars of the analytic hierarchy process (AHP) are presented. These include: (1) ratio scales derived from reciprocal paired comparisons; (2) paired comparisons and the psychophysical origin of the fundamental scale used to make the comparisons; (3) conditions for sensitivity of the eigenvector to changes in judgements; (4) homogeneity and clustering to extend the scale from 1–9 to 1-℞; (5) additive synthesis of priorities, leading to a vector of multi-linear forms as applied within the decision structure of a hierarchy or the more general feedback network to reduce multi-dimensional measurements to a uni-dimensional ratio scale; (6) allowing rank preservation (ideal mode) or allowing rank reversal (distributive mode); and (7) group decision making using a mathematically justifiable way for synthesising individual judgements which allows the construction of a cardinal group decision compatible with individual preferences. These properties of the AHP give it both theoretical support and broad application.

Deriving the AHP 1-9 Scale form First Principles

Abstract: Summary: We demonstrate how the integers 1 to 9 used in the Fundamental Scale of the AHP to represent pairwise comparison judgments can be derived from stimulus-response theory. The conditions required for the stability of the eigenvector of priorities, known from the mathematics literature, are briefly mentioned. These conditions require that the elements being compared be homogeneous. This limits the upper value of the scale to 9. They also require that the number of elements compared be small. It is widely known that both of these conditions are intrinsic to the way in which our brains actually operate. A brief discussion is given about two ways to deal with a large number of elements, both included in the AHP protocol.

The Decision by the US Congress on China’s Trade Status: A Multicriteria Analysis

Abstract: In this paper, we used a decision making tool, the Analytic Hierarchy Process (AHP), to analyze a decision to select a trade status for China that is in the best interest of the United States before that decision came before Congress for a vote.

Forecasting the Future of the Soviet Union

Abstract: In this chapter we report on a study carried out in May of 1990 which uses the AHP to determine the future of the Soviet Union. This question has been of utmost importance to every person alive because of the Soviet Union’s implicit and explicit influence on the future of the world. This work is an attempt to project the outcome of the various forces at work within and outside the Soviet Union that were thought to affect its destiny. Three different scenarios were formulated as possible outcomes. The purpose was not just to predict the future, but to develop a framework where variables involved in this complex problem could be identified, the effect of these variables on shaping the future could be evaluated, and the overall outcomes from these events could be derived. The hope is for identifying some actions to be taken to facilitate the way to peace, to avoid unnecessary violence, and to formulate intelligent and consistent policies.

Hypermatrix of the Brain

Abstract: Decision-making, a natural and fundamental process of the brain, involves the use of pairwise comparisons. They are represented by a matrix whose entries belong to a fundamental scale, and from which an eigenvector of priorities that belongs to a ratio scale is derived. A simple decision is represented by a hierarchic structure, more complex ones by a feedback network. The alternatives from which the choice is made belong to the bottom level of the hierarchy whose upper levels contain the criteria and objectives of the decision. The derived eigenvectors are successively used to synthesize the outcome priorities by weighting and adding. A simple example of choosing the best school for the author’s son is used to illustrate this process. When there is dependence and feedback in a decision, synthesis requires the use of a stochastic supermatrix whose entries are block matrices of column normalized eigenvectors derived from paired comparisons. Stochasticity is ensured by also comparing the influence of the components that give rise to the blocks.

Ratio Scales are Critical for Modeling Neural Synthesis in the Brain

Abstract: The brain generally miniaturizes its perceptions into what may be regarded as a model of what happens outside. We experience the world according to the capacity of our nervous system to register the stimuli we receive. In order to understand and control the environment there needs to be proportionality between the measurements represented in the miniaturized model that arise from the firings of our neurons, and the actual measurements in the real world. Thus our response to stimuli must satisfy the fundamental functional equation F(ax) = bF(x). In other words, our interpretation of a stimulus as registered by the firing of our neurons is proportional to what it would be if it were not filtered through the brain. This equation is the homogeneous part of the inhomogeneous equation F(ax) − bF(x) = G(x) with the forcing function G(x). What interests us here is the mode of operation of the (firing) system that needs to always satisfy the homogeneous part.

The Case of the Spotted Owl vs. The Logging Industry

Abstract: In this chapter we analyze the controversy surrounding the Northern Spotted Owl. This debate has been raging in the United States for five years, particularly in the Pacific Northwest region of the country. On the surface it may appear that the problem is limited to deciding whether or not to fully protect a single species of bird, but in reality this issue has implications that extend much further.

Selection of Recycling Goal Most Likely to Succeed

Abstract: Americans throw out about 160 million tons of garbage a year - 3.5 pounds apiece each day. And, the volume of garbage keeps growing — up by 80% since 1960, and expected to increase by an additional 20 percent by the year 2000. Where we are going to put it all is becoming an item on the nation’s agenda.