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

1. How to Make a Decision. 2. The Seven Pillars of the AHP. 3. Architectural Design. 4. Designing a Mousetrap. 5. Designing the Best Catamaran. 6. The Selection of a Bridge. 7. Measuring Dependence Between Activities: Input Output Application to the Sudan. 8. Technological Choice in Less Developed Countries. 9. Market Attractiveness of Developing Countries. 10. An AHP Based Approach to the Design and Evaluation of a Marketing Driven Business and Corporate Strategy. 11. New Product Pricing Strategy. 12. Incorporating Expert Judgment in Economic Forecasts - the Case of the U.S. Economy in 1992. 13. A New Macroeconomic Forecasting and Policy Evaluation Method. 14. Forecasting the Future of the Soviet Union. 15. Abortion and the States: How Will the Supreme Court Rule on the Upcoming Pennsylvania Abortion Issue. 16. The Benefits and Costs of Authorizing Riverboat Gambling. 17. The Case of the Spotted Owl vs. the Logging Industry. 18. Selection of Recycling Goal Most Likely to Succeed. 19. To Drill or Not to Drill: A Synthesis of Expert Judgments. 20. Modeling the Graduate Business School Admissions Process. 21. Infertility Decision Making. 22. The Decision by the US Congress on China's Trade Status: A Multicriteria Analysis. 23. Deciding Between Angioplasty and Coronary Artery Bypass Surgery. Index.

Models, Methods, Concepts & Applications of the Analytic Hierarchy Process

This paper contains an axiomatic treatment of the Analytic Hierarchy Process AHP. The set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies. The axioms highlight: 1 the reciprocal property that is basic in making paired comparisons; 2 homogeneity that is characteristic of people's ability for making comparisons among things that are not too dissimilar with respect to a common property and, hence, the need for arranging them within an order preserving hierarchy; 3 dependence of a lower level on the adjacent higher level; 4 the idea that an outcome can only reflect expectations when the latter are well represented in the hierarchy. The AHP neither assumes transitivity or the stronger condition of consistency nor does it include strong assumptions of the usual notions of rationality. A number of facts are derived from these axioms providing an operational basis for the AHP.

Axiomatic foundation of the analytic hierarchy process

Decision Making for Leaders is an introduction to Saaty's analytic hierarchy process (AHP) aimed at an audience of leaders in business, industry, and government. As such, the book can be viewed as a popularized version of Saaty's more technical works on AHP (for example, see [1]).

Decision making for leaders

: The Analytic Hierarchy Process serves as a framework for people to structure their own problems and provide their own judgements based on knowledge, reason or feelings, to derive a set of priorities for activities to which they, for example, wish to allocate effort or resources. In this process transitivity of preference is studied through a new approach to consistency - which need not always strictly hold for the results to be acceptable. Also since hierarchic structures may not be complete, not all alternatives need to be directly comparable. It is necessary to construct a pairwise comparison matrix of the relative contribution or impact of each element on each governing objective or criterion in the adjacent upper level. In such a matrix of the elements by the elements, the elements are compared in a pairwise manner with respect to a criterion in the next level. In comparing the i,j elements, people prefer to give a judgement which indicates the dominance as an integer. Thus, if the dominance does not occur in the i,j position while comparing the ith element with the jth element then it is given in the j,i position as a ji and its reciprocal is automatically assigned to aij.

/pdf/optimization-by-the-analytic-hierarchy-process-21i6ln7e11.pdf

Optimization by the Analytic Hierarchy Process

https://www.stat.uchicago.edu/~lekheng/meetings/mathofranking/ref/saaty1.pdf

Thomas L. Saaty

Papers

Models, Methods, Concepts & Applications of the Analytic Hierarchy Process

Axiomatic foundation of the analytic hierarchy process

Decision making for leaders

Optimization by the Analytic Hierarchy Process

Decision-making with the AHP: Why is the principal eigenvector necessary