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

Americans throw out about 160 million tons of garbage a year - 3.5 pounds apiece each day. And, the volume of garbage keeps growing — up by 80% since 1960, and expected to increase by an additional 20 percent by the year 2000. Where we are going to put it all is becoming an item on the nation’s agenda.

Selection of Recycling Goal Most Likely to Succeed

While even a detailed implementation plan will require further discussion between the parties, the participants in our study, who are significant members of the Israeli and Palestinian communities, believe that the level of detail presented below will facilitate agreement on these issues, even if some modifications are required. To develop each of the principles into a working model, we follow the same process used to arrive at the principles described in Chap. 7.

Implementation of the Principles: Getting Down to Earth

President Roosevelt founded Social Security in 1935. In 1937, the Federal Insurance Contribution Act (FICA) was signed and mandated that workers contribute 2 % of wages.

Stabilizing Social Security for the Long-Term

kn + 1, and the integer kn + i = tn! + i, i = 2,..., n 1, is divisible by i and is thus composite. To prove that there exists a largest integer n to which each of its composite totitives can be added to obtain a composite, note first that for n large there exist primes p such that n +p* 0, the inequalities (9) hold with c3 = 1 + e, c4 = 1 E, for all sufficiently large n. This in turn provides the existence of a primep in the interval [n +p*, 2n] such thatp n -O (modp*). Since n <p < 2n, c =p n is a positive composite integer such that c < n and (c, n) = 1. Thus c is a composite totitive of n satisfying n + c =p a prime. The theorem follows since this can be achieved for all large n.

Hoover's Problem

Petroleum exploration is a costly venture which always involves a great deal of uncertainties and unknown factors. A decision to drill could result in a giant discovery, a modest discovery, or a dry hole. The factors influencing drilling decisions could be of geologic, economic and personal nature. When making a decision based on geologic factors alone, geologists and geophysicists will try to find answers to the following questions [2].

Thomas L. Saaty

Papers

Selection of Recycling Goal Most Likely to Succeed

Implementation of the Principles: Getting Down to Earth

Stabilizing Social Security for the Long-Term

Hoover's Problem

To Drill or Not to Drill: A Synthesis of Expert Judgments