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

Representation of visual response to neural firing

Since the founding of Israel in 1947 and even before, there has been conflict and fighting in the Middle East. Hundreds of people including women and children have been killed and thousands injured, hundreds of homes and other properties destroyed. It is a fact that most of the dead, injured, and much of the property lost is Palestinian. Israel feels threatened by acts of terrorism and the Palestinians many of whom live in camps in Lebanon and Jordan, deprived of a national identity feel hopeless, and lacking in freedom and economic well-being. Where will this end? People have always thought that to solve the problem and create a better atmosphere, the Palestinians must have a state. There is little disagreement about that, but there is disagreement about when and what the territories of that state will be. Would that remove the hatred? It is very unlikely. What would diminish the hatred? Giving the Palestinians something constructive within the Palestinian territories like building factories there that can helps them to be profitably occupied individually and as families and groups of people. Instead of spending billions on armament, at least part of these resources along with US and international assistance should be spent on the cause of the conflict and how best to alleviate it into the distant future.

The Most Hopeful Outcome in the Middle East Conflict: The Analytic Network Process Approach

It is known and has been mathematically proven that the principal eigenvector is necessary for deriving priorities from judgments in the Analytic Hierarchy Process (AHP). According to the work of Oskar Perron, the principal eigenvector can be obtained as the limiting power of a positive matrix. In this paper we show that the principal eigenvector does not need the theory of Perron for its existence based on the fact that the principal eigenvalue and corresponding principal eigenvector are transparently obtained for a consistent matrix. By perturbation theory the result is obtained for a near consistent matrix.
http://dx.doi.org/10.13033/ijahp.v5i2.191

The analytic hierarchy process without the theory of oskar perron

Introduction The purpose of this paper is to show how the Analytic Hierarchy Process (AHP) applies mathematics to deal with the most complex problems of the world in a comprehensive and holistic way—in this case the Israeli-Palestinian conflict. This process has been helpful in finding solutions to some of the world’s most complex struggles, including those in South Africa and Northern Ireland. But it has not been used extensively to address the Middle East conflict because of the unique aspects of that struggle. Five years ago, we began preliminary work to organize the excruciatingly difficult issues associated with that six-decades-old confrontation. We began by testing how this retributive conflict (one in which both sides profess to desiring a solution but are equally committed to inflicting pain on the other party) could be profitably addressed by the AHP. This paper should serve as an illustration of how mathematics can help quantify the value of tradeoffs through relative scales (priorities derived from pairwise comparison judgments). The reader can find the mathematical foundations of the theory in an article recently published by the first author in these Notices in February 2013 [3]; see also [4]. Figure 1 shows a map of Israel and Palestine as the borders currently

/pdf/principles-for-implementing-a-potential-solution-to-the-1fkx81ebxf.pdf

Principles for implementing a potential solution to the Middle East Conflict

The United States spends 8.6 percent of its total gross national product (the highest percentage in the world) on health care systems (Sidel and Sidel, 1977); yet it ranks nineteenth in the world in providing care necessary to decrease mortality and morbidity rates. Conversely there are countries such as Great Britain, whose expenditures are closer to 5 percent, that rank higher in the provision of quality medical care (Silver, 1976). Considerable medical expenditure in the United States goes into duplication of equipment and personnel in a single community and even within a single hospital.

Thomas L. Saaty

Papers

Representation of visual response to neural firing

The Most Hopeful Outcome in the Middle East Conflict: The Analytic Network Process Approach

The analytic hierarchy process without the theory of oskar perron

Principles for implementing a potential solution to the Middle East Conflict

Optimum Determination of Hospital Requirements