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.

The Analytic Hierarchy Process

A Scaling Method for Priorities in Hierarchical Structures

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.

https://www.springer.com/productFlyer_978-0-7923-7435-0.pdf?SGWID=0-0-1297-33300503-0

Fuzzy Set Theory - and Its Applications

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

Principles of Neural Science

How to make a decision: The analytic hierarchy process

This paper explores the concept of optimization by solely using the AHP and compares outcomes with those obtained in traditional optimization theory without and with constraints. The difference is essentially in the absence of the traditional black box involving complex manipulations in algebra or the calculus on an assumed linear or nonlinear mathematical structure. This paper is an exploratory attempt to use an individual's understanding together with a way to convert his judgments to ratios to deal with optimization. At first sight it may go contrary to the reader's (learned) intuition, but in the end he must face the question of whether the magic of traditional manipulations gives rise to better answers than one's actual and complete understanding in which one does not abdicate judgmental control of the solution, and why. This idea is ripe for deeper and more detailed exploration.

Exploring optimization through hierarchies and ratio scales

This paper proposes a novel evaluation approach for the selection of candidates for promotion and/or tenure. The decision problem is conceptualized as a hierarchy of factors and a mathematical procedure known as the Analytic Hierarchy Process (AHP) is used for successively "weighting" or prioritizing factors at each level of the hierarchy, in order to arrive at a final composite set of weights for each potential candidate, listed as alternatives at the final level of the hierarchy. The procedure and its mathematical basis are explained and illustrated using hypothetical data. It is argued that the AHP can aid university decision makers in arriving at objective and consistent decisions on faculty tenure, which at present appear to be largely subjective and informal.

http://link.springer.com/content/pdf/10.1007%2FBF00979603.pdf

An objective approach to faculty promotion and tenure analytic hierarchy process by the

An assumption arising from the practice of science and engineering since the middle ages is that because nature is physical, we should be able to relate all measurement to physical dimensions. But that is not true. Human thinking and feeling exist in the physical world but they are not matter or gravity or electromagnetism in the strict sense science understands them today. They are intangible. The human experience involves a very large number of intangibles. In general and with few exceptions, intangibles cannot be measured on a physical scale. However, they can be measured in relative terms through comparison with other tangibles or intangibles with respect to attributes they have in common (taken one at a time) and a ratio scale can be derived from them that yields their relative measurement values. The attributes are themselves compared as to their importance with respect to still higher attributes, relative measures derived, and so on up to an overall goal.

Thomas L. Saaty

Papers

Exploring optimization through hierarchies and ratio scales

An objective approach to faculty promotion and tenure analytic hierarchy process by the

Basic theory of the analytic hierarchy process: how to make a decision

Scientific Method: Optimizing Applied Research Decisions

Dirac distributions and threshold firing in neural networks