Reduction of the Pareto Set An Axiomatic Approach 1st Edition by Vladimir Noghin 3319678728 9783319678726

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Product details:

ISBN 10: 3319678728

ISBN 13: 9783319678726

Author: Vladimir D. Noghin

This book focuses on the issues of decision-making with several numerical criteria. It introduces an original general approach to solving multicriteria problems given quantitative information about the preference relation of a decision-maker. It considers the problems with crisp as well as fuzzy preference relations, accepting the four axioms of “reasonable choice”. Further, it defines the notion of an information quantum about the preference relation of a decision-maker and studies the reduction of the Pareto set using a finite collection of information quanta, demonstrating that the original approach yields a good approximation for the set of nondominated alternatives in a multicriteria problem. Lastly, it analyzes a possible combination of the axiomatic approach with other well-known methods. Intended for a wide range of professionals involved in solving multicriteria problems, including researchers, design engineers, product engineers, developers and analysts, the book is also a valuable resource for undergraduate and postgraduate students of mathematics, economics, and engineering.

Table of contents:

Chapter 1 Edgeworth-Pareto Principle

Chapter 2 Pareto Set Reduction Based on Elementary Information Quantum

Chapter 3 Pareto Set Reduction Based on General Information Quantum

Chapter 4 Pareto Set Reduction Using Elementary Collections of Information Quanta

Chapter 5 Pareto Set Reduction Based on Collections of Information Quanta

Chapter 6 Completeness Property of Information Quanta

Chapter 7 Pareto Set Reduction Using Fuzzy Information

Chapter 8 Decision-Making Based on Information Quanta: Methodology and Practice

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Tags: Vladimir Noghin, Reduction, Pareto, Axiomatic