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

Dependence and independence: From linear hierarchies to nonlinear networks

http://www.isahp.org/2007Proceedings/Papers/Master%20Sessions/Fuzzifying%20Numerical%20Judgements%20in%20AHP.pdf

On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process

Exploring the interface between hierarchies, multiple objectives and fuzzy sets

This paper presents a summary of the discrete mathematical part of my work, the Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP), for measuring tangible and intangible factors, particularly as applied to decision making. The factors of the decision are arranged in hierarchical or network structures and judgments are then made by the decision maker, or by an expert, about the dominant element for each pair with respect to a common property. From simple judgments on two elements at a time with respect to a common property, priority vectors are obtained that are combined throughout the structure to give the best outcome for a decision. The judgments may be inconsistent, and there is a mathematical way to measure inconsistency so that the outlying judgments may be revised by the decision maker in an acceptable way or a decision may be delayed until more consistent information is obtained. In practical applications using either hierarchical ...

Thomas L. Saaty

Papers

Dependence and independence: From linear hierarchies to nonlinear networks

On the invalidity of fuzzifying numerical judgments in the Analytic Hierarchy Process

Exploring the interface between hierarchies, multiple objectives and fuzzy sets

The Modern Science of Multicriteria Decision Making and Its Practical Applications: The AHP/ANP Approach

Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios