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.

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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

What is relative measurement? The ratio scale phantom

A new macroeconomic forecasting and policy evaluation method using the analytic hierarchy process

On polynomials and crossing numbers of complete graphs

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.

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

This paper gives a brief overview of the well-known impossibility-possibility theorem in constructing a social welfare function from individual functions. The Analytic Hierarchy Process uses a fundamental scale of absolute numbers to represent judgments about dominance in paired comparisons. It is shown that it is possible to derive such a function in two ways. One is from the synthesized functions of the judgments of each of the individuals. The other is obtained by first combining corresponding pairwise comparison judgments made by all the individuals, thus obtaining a matrix of combined judgments for the group and then deriving a welfare function for the group. With consistency the four conditions imposed by Arrow are satisfied. With inconsistency, an additional condition is needed.

Thomas L. Saaty

Papers

What is relative measurement? The ratio scale phantom

A new macroeconomic forecasting and policy evaluation method using the analytic hierarchy process

On polynomials and crossing numbers of complete graphs

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

The possibility of group welfare functions