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

It is shown here that one cannot simply take columns of numbers, normalize them and add to obtain results corresponding to operations in the AHP. This is what traditional expected value theory using a single scale would lead one to do. Care needs to be exercised. What one must do is to interpret the data represented by each column according to relative importance to a decision maker so that the alternatives under each criterion are pairwise compared according to the fundamental scale used to represent judgments. This procedure then leads to a set of vectors which belong to the same ratio scale and they can now be combined by using the weights of the criteria.

A note on the AHP and expected value theory

Scaling the membership function

SUMMARY Models for growth distributions of biological organisms are investigated in this paper. They are specializations of the birth-death equations with two absorbing barriers. The solutions we seek are the distributions of the time to grow from an initial dose to an infective dose. Equations for these functions are simply obtained from the birth-death equations. Two main cases of interest are then examined. In the first case the birth and death rates are proportional to the number present and in the second case they are constant. Graphs are developed for the solution of the first case. Useful applications depend on this result.

Some Stochastic Processes with Absorbing Barriers

Publisher Summary
This chapter discusses the rationale for systems thinking, causal explanation on how reductionism works, past and present systems theory, and the conceptual value of systems theory to provide an overview of systems. Despite the philosophical appeal of looking at a problem from many points of view, the solution of any problem will finally follow a certain plan with a defined line of thinking. As a result, it is difficult to argue against reductionism without offering a better alternative. Pragmatic systems research synthesizes reductionism and expansionism by first conceptualizing problems in terms of their systemic characteristics and then identifying those components that have the greatest influence in the system. In other words, the systems approach must draw on innate abilities to decompose complex phenomena into component elements while simultaneously conceptualizing and identifying relations of varying intensity among the elements of the system. Still systems theory has so far been criticized for its lack of a viable methodology. Despite its shortcomings, systems theory has provided a conceptual foundation on which to construct a new methodology that allows describing a system and its problems in terms of an interconnected hierarchy. It also offers a means to set a priority order and measure the intensity of interaction of the components of the hierarchy describing the structure of a system. This methodology considers the human element of complex social and organizational problems and accommodates multiple conflicting goals and objectives held by people whose interests are affected by the performance of the system.

Thomas L. Saaty

Papers

A note on the AHP and expected value theory

Scaling the membership function

Some Stochastic Processes with Absorbing Barriers

CHAPTER 2 – Systems

The Simplex Method of Linear Programming.