ENGLISH

Reduction of the Pareto set : an axiomatic approach

By Noghin , Vladimir D

Book information

Publisher
Springer
Year
2018
ISBN
978-3-319-67873-3, 3319678736, 978-3-319-67872-6
Language
english
Format
PDF
Filesize
4 MB (4182496 bytes)
Series
Studies in systems decision and control 126
Pages
\248
Time added
2017-10-15 16:00:00
Axiomatic set theory;Multiple criteria decision ma

Description

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. Front Matter ....Pages i-xix Edgeworth-Pareto Principle (Vladimir D. Noghin)....Pages 1-22 Pareto Set Reduction Based on Elementary Information Quantum (Vladimir D. Noghin)....Pages 23-50 Pareto Set Reduction Based on General Information Quantum (Vladimir D. Noghin)....Pages 51-66 Pareto Set Reduction Using Elementary Collections of Information Quanta (Vladimir D. Noghin)....Pages 67-95 Pareto Set Reduction Based on Collections of Information Quanta (Vladimir D. Noghin)....Pages 97-138 Completeness Property of Information Quanta (Vladimir D. Noghin)....Pages 139-149 Pareto Set Reduction Using Fuzzy Information (Vladimir D. Noghin)....Pages 151-178 Decision-Making Based on Information Quanta: Methodology and Practice (Vladimir D. Noghin)....Pages 179-222 Back Matter ....Pages 223-232

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