Thomas L. Saaty

Bio: Thomas L. Saaty is an academic researcher from University of Pittsburgh. The author has contributed to research in topics: Analytic hierarchy process & Analytic network process. The author has an hindex of 92, co-authored 375 publications receiving 95026 citations. Previous affiliations of Thomas L. Saaty include College of Business Administration & Politécnico Grancolombiano.

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.

Analytic Hierarchy Process

Abstract: The Analytic Hierarchy Process (AHP) is a theory of relative measurement of intangible criteria. With this approach to relative measurement, a scale of priorities is derived from pairwise comparison measurements only after the elements to be measured are known. The ability to do pairwise comparisons is our biological heritage and we need it to cope with a world where everything is relative and constantly changing and thus, there are no fixed standards to measure things on. In traditional measurement, one has a scale that one applies to measure any element that comes along that has the property the scale is for, and the elements are measured one by one, not by comparing them with each other. In the AHP, paired comparisons are made with judgments using numerical values taken from the AHP absolute fundamental scale of 1 to 9. A scale of relative values is derived from all these paired comparisons and it also belongs to an absolute scale that is invariant under the identity transformation like the system of real numbers. The AHP is useful for making multicriteria decisions involving benefits, opportunities, costs, and risks. The ideas are developed in stages and illustrated with examples of real-life decisions. The subject is transparent and easy to understand why it is done the way it is along the lines discussed here. The AHP has a generalization to dependence and feedback; the Analytic Network Process (ANP) is not discussed here. Keywords: analytic hierarchy process; decision making; prioritization; benefits; costs; complexity

An exposition of the AHP in reply to the paper “remarks on the analytic hierarchy process”

Abstract: It is a fact that people make decisions and have been making decisions for a very long time. Contrary to what some of us who are interested in decision-making may like to believe, most people do not take seriously the existence of theories which purport to set their thinking and feeling right. They claim to know their own value system and what they want. They may wonder how anyone else can know well enough to tell them how best to organize their thinking in order to make better choices. Yet, research has shown that complex decisions are beyond the capacity of the brain to synthesize intuitively and efficiently. Since decision making is a natural characteristic of people, how do we describe what they do so that an ordinary mortal can understand what we are saying? We do not wish to legislate the method with which people should make decisions, but only to describe it even when it is prescribed by some method. In the process, we may learn things that can help people make better decisions. How? The Analytic Hierarchy Process (AHP) (Forman et al., Harker 1986, Harker and Vargas 1987, Saaty 1986, 1988a, b, Saaty and Vargas 1987, Xu 1988, Golden et al. 1989, Saaty and Alexander 1989) is a theory of measurement. When applied in decision making it assists one to describe the general decision operation by decomposing a complex problem into a multi-level hierarchic structure of objectives, criteria, subcriteria and alternatives. The AHP provides a fundamental scale of relative magnitudes expressed in dominance units to represent judgments in the form of paired comparisons. A ratio scale of relative magnitudes expressed in priority units is then derived from each set of comparisons. An overall rcatio scale of priorities is then synthesized to obtain a ranking of the alternatives. From its axioms to its procedures, the AHP has turned out to be historically and theoretically a different and independent theory of decision making from utility theory. Much as a dialogue evolved in mathematics around the consistency of different geometries and around absolute and relative space and time in physics, both to dispel absolute notions, those who believe that only utility theory can tell us the absolute truth about man's decision-making might take a close look at the AHP. It has found varied and serious applications. It also has a particular way of generating ratio scales and dealing with inconsistency in judgment that have contributed to its effectiveness in resource allocation and in the setting of priorities by a group of decision makers. Utility theory is a normative process. The AHP as a descriptive theory encompasses procedures leading to outcomes as would be ranked by a normative theory. But it must go beyond to deal with outcomes not accounted for by the demanding assumptions of a normative theory. We must briefly describe the AHP to enable the reader to see that a practicable theory based on ratio scales need not dilute itself to satisfy expectations of people who derive their understanding from a theory based on interval scales. This is particularly true if the rival theory, in aspiring for generality, also makes unrealistic assumptions, for example about the transitivity and consistency of preferences and the difficult use of lotteries,

The Analytic Hierarchy Process

Abstract: This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.

Fuzzy Set Theory - and Its Applications

Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.

Principles of Neural Science

Abstract: I have developed "tennis elbow" from lugging this book around the past four weeks, but it is worth the pain, the effort, and the aspirin. It is also worth the (relatively speaking) bargain price. Including appendixes, this book contains 894 pages of text. The entire panorama of the neural sciences is surveyed and examined, and it is comprehensive in its scope, from genomes to social behaviors. The editors explicitly state that the book is designed as "an introductory text for students of biology, behavior, and medicine," but it is hard to imagine any audience, interested in any fragment of neuroscience at any level of sophistication, that would not enjoy this book. The editors have done a masterful job of weaving together the biologic, the behavioral, and the clinical sciences into a single tapestry in which everyone from the molecular biologist to the practicing psychiatrist can find and appreciate his or