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.

Mathematics of the brain: generalization from Eigen vectors to eigen functions.

Abstract: In this paper, we provide an overview of the mathematics of the brain and present the generalization from Eigen vectors to Eigen functions. Initially we summarize some of the mathematics of derived priority scales involved in the multicriteria decision process, and give the corresponding generalization to the continuous case. Then we discuss of density and approximation and how we can generalize from discrete to continuous judgments. The solutions of the functional equation w(as)=bw(s) are given in the real and complex domain and then for quaternions (non-commutative) and octonions (non-commutative and non-associative). In the end we present the consequences and evidence for validation: a) The Laws of Nature are written in the Workings of our Brains, b) the Weber-Fechner Law of Psychophysics, and c) The Brain Works with Impulsive Firings.

The serious omission of comparisons in aristotle's law of thought

Abstract: Saaty lecturing at ISAHP2011 in Sorrento, Italy. Comparisons are the bedrock of all human thinking no matter where it is done on this earth in every culture. We compare things with one another and with themselves through memory to know if they are what we are looking for. We need memory and time to do that regardless of how brief and spontaneous a comparison may be. Thus thought is a dynamic process in its minutest form and needs time to be connected and unfolded to draw meaning as we compare it to other thoughts.http://dx.doi.org/10.13033/ijahp.v3i2.124

Integrating the Analytic Network Process and the Balanced Scorecard for Strategic IT Outsourcing Decision Making

Abstract: In outsourcing, management seeks to achieve costs savings, operational efficiency, customer satisfaction, and/or company growth. We integrate the ANP with the perspectives in Balanced Scorecard (BSC) for IT outsourcing decision making. The proposed BSC-ANP model helps evaluate the impact of decision on firm performance and confirms the existence of indicator interactions.

Rank Preservation and Reversal in Decision Making

Abstract: There are numerous real life examples done by many people which show that the alternatives of a decision sometimes can reverse their original rank order when new alternatives are added or old ones deleted and without bringing in new criteria. There is no mathematical theorem which proves that rank must always be preserved and there cannot be because of real life and hypothetical counter examples in decision making methods. Rank preservation came to be accepted as the standard because of techniques that could only rate alternatives one at a time treating them as independent. Thus an alternative receives a score and it will not change when other alternatives are added or deleted. All methods that only rate alternatives one at a time, thus always preserving rank, may not lead to the right decision; even if they may be right in certain areas of application. In reality, to determine how good an alternative is on an intangible criterion needs experience and knowledge about other alternatives and hence in their evaluation, the alternatives cannot be completely considered as independent of one another.

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