Thinking With Models: Mathematical Models in the Physical, Biological and Social Sciences (V. 2)

Science & Math

Thomas L. Saaty

Joyce M. Alexander

Mathematics

Pergamon Pr

This note from Prof. Vargas regarding a competitive title by Prof. Saaty with an almost identical title (THEORY AND APPLICATIONS OF THE ANALYTIC NETWORK PROCESS: Decision Making with Benefits, Opportunities, Costs, and Risks. RWS Publications, 2005):  "The other book is theoretical with passing mention of examples to show how the subject is used. In our book (the one you have) the applications are different and given in full detail relevance and originality. They have never appeared in print as they are here and most users would prefer them to the theoretical book. In addition chapter 1 summarizes the theory given in four chapters on the book showing the important parts without going into too much detail. I would rather read this book than the other one definitely and this could not have been done so elegantly had not the other been written before. Therefore this book has the cream of the ideas and the best published applications so far." 

Decision Making with the Analytic Network Process: Economic, Political, Social and Technological Applications with Benefits, Opportunities, Costs and ... in Operations Research & Management Science)

Business & Money

Economics

Springer

"We are surrounded and deeply involved, in the natural world, with nonlinear events which are not necessarily mathematical," the authors write. "For example … the nonlinear problem of pedaling a bicycle up and down a hillside. On a grand scale … the struggle for existence between two species, one of which preys exclusively on the other." This book is for mathematicians and researchers who believe that "nonlinear mathematics is the mathematics of today"; it is also for economists, engineers, operations analysts, "the reader who has been thus bemused into an artificially linear conception of the universe." Nonlinear Mathematics is the first attempt to consider the widest range of nonlinear topic found in the scattered literature. Accessible to nonmathematics professionals as well as college seniors and graduates, it offers a discussion both particular and broad enough to stimulate research toward a unifying theory of nonlinear mathematics. Ideas are presented "according to existence and uniqueness theorems, characterization (e.g., stability and asymptotic behavior), construction of solutions, convergence, approximation, and errors." Contents include: Linear and nonlinear transformations Nonlinear algebraic and transcendental equations Nonlinear optimization; nonlinear programming and systems of inequalities Nonlinear ordinary differential equations Introduction to automatic control and the Pontryagin principle Linear and nonlinear prediction theory Exercises are given as guides through theorem proofs and methodology. Extensive bibliographies are appended to each section. "We have tried," write the authors, "to give more than a compilation of known techniques, to convey a spirit. In this spirit we integrate different topics of mathematics to show their interrelations, to stimulate inventiveness through variety, and to emphasize their origins from interaction with natural phenomena in physics, engineering, and economics." This examination of nonlinear mathematics gives a panoramic introduction (suitable for self-study) to a crucial field in contemporary research.

Nonlinear Mathematics (Dover Books on Mathematics)

Joseph Bram

Dover Publications

Models, Methods, Concepts and Applications of the Analytic Hierarchy Process is a volume dedicated to selected applications of the Analytic Hierarchy Process (AHP) focused on three themes: economics, the social sciences, and the linking of measurement with human values. (1) The AHP offers economists a substantially different approach to dealing with economic problems through ratio scales. The main mathematical models on which economics has based its quantitative thinking up to now are utility theory, which uses interval scales, and linear programming. We hope that the variety of examples included here can perhaps stimulate researchers in economics to try applying this new approach. (2) The second theme is concerned with the social sciences. The AHP offers psychologists and political scientists the methodology to quantify and derive measurements for intangibles. We hope that the examples included in this book will encourage them to examine the methods of AHP in terms of the problems they seek to solve. (3) The third theme is concerned with providing people in the physical and engineering sciences with a quantitative method to link hard measurement to human values. In such a process one needs to interpret what the measurements mean. A number is useless until someone understands what it means. It can have different meanings in different problems. Ten dollars are plenty to satisfy one's hunger but are useless by themselves in buying a new car. Such measurements are only indicators of the state of a system, but do not relate to the values of the human observers of that system. AHP methods can help resolve the conflicts between hard measurement data and human values.

Models, Methods, Concepts & Applications of the Analytic Hierarchy Process (International Series in Operations Research & Management Science)

Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World

Management & Leadership

Rws Pubns

Multicriteria Decision Making

Reference

Book by Saaty, Thomas L., Kearns, Kevin P., Vargas, Luis G.

Analytical Planning/the Logic of Priorities

This book is a dictionary of over 400 decision problems in government and the private sector, structured as hierarchical decision models. The Hierarchon serves as a stimulus, a rich source of ideas to help in structuring decision problems as hierarchies.

The Hierarchon: A Dictionary of Hierarchies (Analytic Hierarchy Process, Vol 5)

RWS Publications

This book is a comprehensive summary, primarily of the author's own thinking and research, about the Analytic Hierarchy Process and decision making. It includes advanced mathematical theory and diverse applications. Fundamentals of Decision Making has all the latest theoretical developments in the AHP and new theoretical material not published elsewhere. We consider this book to be the replacement for the original book on the subject, The Analytic Hierarchy Process that was published by McGraw Hill Publishers, New York.

Fundamentals of Decision Making and Priority Theory (Analytic Hierarchy Process Series, Vol. 6)

This book is about how to make decisions using the Analytic Hierarchy Process. The basics of the theory are described in a clear, non-technical manner with many examples. It is suitable for business leaders and also is probably the best book for introducing the AHP to students at the college and graduate level. In this fifth printing of the book the reader will find a new appendix containing real-life applications that validate the use of the fundamental scale of the AHP.

Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World, New Edition 2001 (Analytic Hierarchy Process Series, Vol. 2)

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Books by Thomas L. Saaty