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

Scenarios and priorities in transport planning: Application to the Sudan

We give a summary and an example of a new, systems oriented, method for estimating the input-output coefficients of a given economy. Our approach is based on pairwise comparisons among the sectors of the economy ranking them according to their priority on a ratio scale[l]. What we obtain corresponds closely to what is computed by traditional methods, but a major advantage to hierarchical measurement is that it does not require extensive use of details to capture the significant relations among the sectors. We shall illustrate here that the general understanding one has about interactions in an economic system is often adequate for making estimates of input-output coefficients without the use of an enormous amount of data. This is particularly useful in cases where market prices do not provide a clear indication of the relative impacts of the various sectors. We wish to point out that the table obtained in this way should be interpreted as a first step in the estimation process and is not a substitute for what one can obtain by thorough and deep analysis by refined methods. However, when one is limited in time and resources and when sufficient data are unavailable, but still one needs an estimate, this is an effective approach and has rigorous underlying mathematical justification. We now summarize some of the main ideas of our approach. Measurement evolves out of comparisons, particularly pairwise comparisons. The scale most desired for the values it yields is the ratio scale (invariant under positive similarity transformations). Let us suppose that we have n objects A,, , A, whose vector of corresponding weights w = (w,, , w.) is known. Let us form the matrix of pairwise comparisons of weights

Estimating technological coefficients by the analytic hierarchy process

https://link.springer.com/content/pdf/10.1057%2Fjors.1991.176.pdf

Response to Holder's Comments on the Analytic Hierarchy Process

In Part 1 (Saaty, T. L., S. I. Gass. 1954. Parametric objective function (Part 1). J. Opns. Res. Soc. Am. 2 316.), the cost function in the general linear programming problem was parametrized with one parameter and the problem of generating solutions completely studied. In Part 2, a generalization to the n-parameter case is outlined, with special emphasis on the two-parameter case. An example is supplied for this case. Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.

Parametric Objective Function (Part 2)—Generalization

Introduction Nearly all of us have been brought up to believe that clear-headed logical thinking is our only sure way to face and solve problems. But experience suggests that logical thinking is not natural to us. Indeed, we have to practice, and for a long time, before we can do it well. Since complex problems usually have many related factors, traditional logical thinking leads to sequences of ideas so tangled that the best solution cannot be easily discerned. For a very long time people believed and argued strongly that it is impossible to express the intensity of human feelings with numbers. The epitome of such a belief was expressed by A. F. MacKay who writes [12] that pursuing the cardinal approaches is like chasing what cannot be caught. It was also expressed by Davis and Hersh [5]: “If you are more of a human being, you will be aware there are such things as emotions, beliefs, attitudes, dreams, intentions, jealousy, envy, yearning, regret, longing, anger, compassion and many others. These things—the inner world of human life— can never be mathematized.” In their book [11]

https://www.ams.org/jourcgi/jour-getitem?pii=noti944

Thomas L. Saaty

Papers

Scenarios and priorities in transport planning: Application to the Sudan

Estimating technological coefficients by the analytic hierarchy process

Response to Holder's Comments on the Analytic Hierarchy Process

Parametric Objective Function (Part 2)—Generalization

On the measurement of intengibles. a principal Eigenvector approach to relative measurement derived from paired comparisons