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

Publisher Summary
Strategic, adaptive planning is a process of learning and growth. It is an ongoing event kept in the foreground to be seen, studied, used as a guide, and revised as change is noted in the environment. Strategic planning is the process of projecting the likely or logical future—the composite scenario—and of idealizing desired futures. It is the process of knowing how to attain these futures, using this knowledge to steer the logical future toward a more desired one, and then repeating the operation. The backward process of idealization inspires creative thinking. It affords people an opportunity to expand their awareness of what states of the system they would like to see take place and with what priorities. Using the backward process, planners identify both opportunities and obstacles and eventually select effective policies to facilitate reaching the desired future. This chapter demonstrates the way in which the systems approach of the Analytic Hierarchy Process (AHP) can be used to plan for likely and desired futures.

CHAPTER 6 – Strategic Planning

Highlights are given of the decision making theory the Analytic Hierarchy Process (AHP) and its generalization to dependence and feedback, the Analytic Network Process (ANP) both of which deal with the measurement of tangible and intangible criteria in relative terms by using paired comparisons. The fundamental scale of absolute numbers for representing judgments is introduced and the principal right eigenvector is shown to be the necessary vector of priorities derived from the possibly inconsistent matrix of comparisons of homogeneous elements. A method of synthesis of priorities is proposed. Rank preservation and reversal are discussed. When independent, the alternatives can be rated one at a time with respect to the criteria using intensities. Negative priorities are also introduced. This paper will be followed soon by two other papers.

/pdf/theory-of-the-analytic-hierarchy-process-part-2-1-4q9t1jl0g4.pdf

Theory of the Analytic Hierarchy Process. Part 2.1

Decisions involving several criteria and alternatives need a correct procedure to combine weights to make tradeoffs and select the best alternatives. There are two parts to the problem, both of which need proof. The first is how to generate judgments and associate numbers with them, and the second is how to combine these numbers in a meaningful way to get an answer.

Some mathematical topics in the analytic hierarchy process

The AHP/ANP are multicriteria decision-making theories that deal with both hierarchic structures when the criteria are independent of the alternatives and with networks when there is any dependence within and between elements of the decision. Both of them have been repeatedly used in practice by various researchers and practitioners. From the perspective of almost 40 years of practice in solving problems using both theories, some of their properties seem to be more important than others. The article indicates four of them as fundamental for understanding AHP/ANP. These are the axioms related to structure, computation, and expectation. The mathematical formulation of the axioms is preceded by an introduction explaining the motivation behind the introduced concepts. The article is expository and it is an improved and refined version of the work [1].

Thomas L. Saaty

Papers

CHAPTER 6 – Strategic Planning

Theory of the Analytic Hierarchy Process. Part 2.1

Some mathematical topics in the analytic hierarchy process

Axioms of the Analytic Hierarchy Process (AHP) and its Generalization to Dependence and Feedback: The Analytic Network Process (ANP).

A natural way to make momentous decisions