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.

The Analytic Hierarchy and Analytic Network Measurement Processes: The Measurement of Intangibles

Abstract: Multicriteria thinking demonstrates that in order to make a best choice in a decision, discussion and cause-effect reasoning are inadequate to learn what the best overall outcome is. The Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP), provide a comprehensive structure and mathematics to incorporate measurements for tangible criteria and derive priorities for intangible criteria to enable one to choose a best alternative for a decision. It overcomes so-called bounded rationality that is based on the assumption of transitivity by including in its structures and calculations, the sensitivity and depth of feelings associated with understanding and the imagination and awareness needed to address all the concerns. The AHP can cope with the inherent subjectivity in all decision making, and make it explicit to the stakeholders through relative quantitative priorities. It also provides the means to validate outcomes when measurements are available to show that it does not do number crunching without meaningful justification. It can deal with the benefits, opportunities, costs and risks separately and bring them together to determine the best overall outcome. One can also perform dynamic sensitivity analysis of changes in judgments to ensure that the best outcome is stable. In an award from the Institute for Operations Research and the Management Sciences (INFORMS) given to the author in October 2008 it is written: “The AHP has revolutionized how we resolve complex decision problems... the AHP has been applied worldwide to help decision makers in every conceivable decision context across both the public and private sectors, with literally thousands of reported applications.”

Rank According to Perron: A New Insight

Abstract: If A = (aij), aij > 0, i, j = 1,. .., n, Perron [4] proved that A has a real positive eigenvalue Xmax (called the principal eigenvalue of A) that is unique, and Xmax > lXkl for the remaining eigenvalues of A. Furthermore, the principal eigenvector w = (wl,..., wn) that is a solution of Aw= Xmaw is unique to within a multiplicative constant and wi > 0, i = 1,..., n. We can make the solution w unique through normalization. We define the norm of the vector w as IIw II = we where e = (1, 1,..., 1)', eT is its transpose, and to normalize w is to divide it by its norm. We shall always think of w in normalized form. Perron's result has found wide use in many areas, both theoretical and applied. Among these are applications to multicriterion decisions. In a recent article in this journal [1], Barbeau gave a lucid exposition and illustrated the use of the Analytic Hierarchy Process (AHP) to assist a college in interpreting grades and testing students for admission. The AHP, which I developed, uses Perron's principal eigenvector as an essential property for determining the preference ranking among a set of alternatives when the judgments are inconsistent. In the AHP the alternatives are compared in pairs with respect to a common attribute in a positive reciprocal matrix whose entries represent the numerical value of the relative preference for one (the row) over another (the column). The reader is referred to Barbeau's paper for a concise reference to the AHP. My purpose in this note is to show how important the principal eigenvector is in determining the rank of the alternatives through dominance walks. Suppose we wish to rate five teachers A, B, C, D, and E according to their excellence in teaching. We enter our evaluation in the following matrix, whose principal eigenvector has been normalized:

Applications of analytic network process in entertainment

Abstract: In this paper we present a real application of ANP in entertainment business, the expansion of Disney amusing parks by establishing a new theme park in greater China. The Analytic Network Process (ANP) is an efficient approach for this critical decision making. ANP is a generalization of the Analytic Hierarchy Process (AHP). The basic structure is an influence network of clusters and nodes contained within the clusters. Priorities are established in the same way they are in the AHP using pairwise comparisons and judgment.

Fuzzy Judgments and Fuzzy Sets

Abstract: Using fuzzy set theory has become attractive to many people. However, the many references cited here and in other works, little thought is given to why numbers should be made fuzzy before plunging into the necessary simulations to crank out numbers without giving reason or proof that it works to one’s advantage. In fact it does not often do that, certainly not in decision making. Regrettably, many published papers that use fuzzy set theory presumably to get better answers were not judged thoroughly by reviewers knowledgeable in both fuzzy theory and decision making. Buede and Maxwell (1995), who had done experiments on different ways of making decisions, found that fuzzy does the poorest job of obtaining the right decision as compared with other ways. “These experiments demonstrated that the MAVT (Multiattribute Value Theory) and AHP (Analytic Hierarchy Process) techniques, when provided with the same decision outcome data, very often identify the same alternatives as ‘best’. The other techniques are noticeably less consistent with the Fuzzy algorithm being the least consistent.â€

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