An Introduction to Decision Theory

With technological advance, the difficulties faced by decision makers and researchers become even more complex and hence more difficult to understand and manage. Traditional approaches have their limitations, particularly when dealing with issues that span many fields of endeavor. Fortunately there has emerged, particularly over the past four decades, the discipline of systems science, which provides a framework for dealing with such complexity.

This comprehensive edited volume is the first of its kind, designed to serve as a textbook for long-duration business analytics programs. It can also be used as a guide to the field by practitioners. The book has contributions from experts in top universities and industry. The editors have taken extreme care to ensure continuity across the chapters.

This book has two main objectives:
• to provide a concise introduction to nonlinear optimization methods, which can be used as a textbook at a graduate or upper undergraduate level;

The monograph offers a view on Rough Mereology, a tool for reasoning under uncertainty, which goes back to Mereology, formulated in terms of parts by Lesniewski, and borrows from Fuzzy Set Theory and Rough Set Theory ideas of the containment to a degree. The result is a theory based on the notion of a part to a degree.

This book is intended to provide an introductory text of Nonlinear and Dynamic Programming for students of managerial economics and operations research. The author also hopes that engineers, business executives, managers, and others responsible for planning of industrial operations may find it useful as a guide to the problems and methods treated, with a view to practical applications. The book may be considered as a sequel to the author's Linear Programming in Industry (1960, 4th revised and enlarged edition 1974), but it can be used independently by readers familiar with the elements of linear programming models and techniques. The two volumes con­ stitute an introduction to the methods of mathematical programming and their application to industrial optimization problems. The author feels that the vast and ever-increasing literature on mathematical programming has not rendered an introductory exposition super­ fluous. The general student often tends to feel somewhat lost if he goes straight to the special literature; he will be better equipped for tackling real problems and using computer systems if he has acquired some previous training in constructing small-scale programming models and applying standard algorithms for solving them by hand. The book is intended to provide this kind of training, keeping the mathematics at the necessary minimum. The text contains numerous exercises. The reader should work out these problems for himself and check with the answers given at the end of the book. The text is based on lectures given at the University of Copenhagen.