Showing papers by "Thomas L. Saaty published in 2008"

Decision making with the analytic hierarchy process

Abstract: Decisions involve many intangibles that need to be traded off To do that, they have to be measured along side tangibles whose measurements must also be evaluated as to, how well, they serve the objectives of the decision maker The Analytic Hierarchy Process (AHP) is a theory of measurement through pairwise comparisons and relies on the judgements of experts to derive priority scales It is these scales that measure intangibles in relative terms The comparisons are made using a scale of absolute judgements that represents, how much more, one element dominates another with respect to a given attribute The judgements may be inconsistent, and how to measure inconsistency and improve the judgements, when possible to obtain better consistency is a concern of the AHP The derived priority scales are synthesised by multiplying them by the priority of their parent nodes and adding for all such nodes An illustration is included

Relative measurement and its generalization in decision making why pairwise comparisons are central in mathematics for the measurement of intangible factors the analytic hierarchy/network process

Abstract: According to the great mathematician Henri Lebesgue, making direct comparisons of objects with regard to a property is a fundamental mathematical process for deriving measurements. Measuring objects by using a known scale first then comparing the measurements works well for properties for which scales of measurement exist. The theme of this paper is that direct comparisons are necessary to establish measurements for intangible properties that have no scales of measurement. In that case the value derived for each element depends on what other elements it is compared with. We show how relative scales can be derived by making pairwise comparisons using numerical judgments from an absolute scale of numbers. Such measurements, when used to represent comparisons can be related and combined to define a cardinal scale of absolute numbers that is stronger than a ratio scale. They are necessary to use when intangible factors need to be added and multiplied among themselves and with tangible factors. To derive and synthesize relative scales systematically, the factors are arranged in a hierarchic or a network structure and measured according to the criteria represented within these structures. The process of making comparisons to derive scales of measurement is illustrated in two types of practical real life decisions, the Iran nuclear show-down with the West in this decade and building a Disney park in Hong Kong in 2005. It is then generalized to the case of making a continuum of comparisons by using Fredholm’s equation of the second kind whose solution gives rise to a functional equation. The Fourier transform of the solution of this equation in the complex domain is a sum of Dirac distributions demonstrating that proportionate response to stimuli is a process of firing and synthesis of firings as neurons in the brain do. The Fourier transform of the solution of the equation in the real domain leads to nearly inverse square responses to natural influences. Various generalizations and critiques of the approach are included.

The Analytic Network Process

Abstract: Analysis to break down a problem into its constituent components to study their behavior has been the major tool of scientific inquiry to test hypotheses and solve problems. It has proven to be extremely successful in dealing with the world of matter and energy. It has enabled man to land on the moon, to harness the energy of the atom, to master global communication, to invent the computer and to produce tens of thousands of useful and not so useful things. But it has not been so effective in the world of man.

Making decisions in hierarchic and network systems

Abstract: This paper summarises a mathematical theory of the measurement of both tangible and intangible factors, the Analytic Hierarchy Process (AHP) and its generalisation to dependence and feedback, the Analytic Network Process (ANP) and illustrates their application to making complex multicriteria decisions.

Synthesis of Complex Criteria Decision Making: A Case Towards a Consensus Agreement for a Middle East Conflict Resolution

Abstract: The Middle East conflict is not a series of wars tending toward peace, but a state of continued belligerency interrupted by war. It is not a single isolated problem to be solved but a system of people with conflicting aspirations. Physically, the problem is geographic with two parties desiring the same piece of land, but its origins are deeply rooted in people’s beliefs and in their attachments to a land consecrated by their great religions.

Who won the 2008 Olympics? A multicriteria decision of measuring intangibles

Abstract: It often happens that at the end of Olympics games the medals won by more than one country are many and close in total number as in the 2008 games where China won 100 medals with many gold ones and the United States won 110 medals but with a lesser number of gold medals. The question is: Although it is often done arbitrarily, is there a way to quantify the values of gold, silver and bronze medals legitimately to resolve this concern? This short exposition shows that there is by using the author’s theory for the measurement of intangibles, the Analytic Hierarchy Process.