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Reduction of the Pareto Set

An Axiomatic Approach

  • Book
  • © 2018

Overview

Authors:
  1. Vladimir D. Noghin

    1. Department of Control Theory, Saint Petersburg State University, Saint Petersburg, Russia

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  • Focuses on the issues of decision-making with several numerical criteria
  • Introduces an original general approach to the solution of multicriteria problems given quantitative information about the preference relation of a decision-maker
  • Intended for a wide range of professionals involved in solving multicriteria problems, including researchers, design engineers, product engineers, developers and analysts
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Systems, Decision and Control (SSDC, volume 126)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Edgeworth-Pareto Principle

    • Vladimir D. Noghin
    Pages 1-22

  3. Pareto Set Reduction Based on Elementary Information Quantum

    • Vladimir D. Noghin
    Pages 23-50

  4. Pareto Set Reduction Based on General Information Quantum

    • Vladimir D. Noghin
    Pages 51-66

  5. Pareto Set Reduction Using Elementary Collections of Information Quanta

    • Vladimir D. Noghin
    Pages 67-95

  6. Pareto Set Reduction Based on Collections of Information Quanta

    • Vladimir D. Noghin
    Pages 97-138

  7. Completeness Property of Information Quanta

    • Vladimir D. Noghin
    Pages 139-149

  8. Pareto Set Reduction Using Fuzzy Information

    • Vladimir D. Noghin
    Pages 151-178

  9. Decision-Making Based on Information Quanta: Methodology and Practice

    • Vladimir D. Noghin
    Pages 179-222

  10. Back Matter

    Pages 223-232
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Control Theory, Saint Petersburg State University, Saint Petersburg, Russia

    Vladimir D. Noghin

Bibliographic Information

  • Book Title: Reduction of the Pareto Set

  • Book Subtitle: An Axiomatic Approach

  • Authors: Vladimir D. Noghin

  • Series Title: Studies in Systems, Decision and Control

  • DOI: https://doi.org/10.1007/978-3-319-67873-3

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing AG 2018

  • Hardcover ISBN: 978-3-319-67872-6Published: 06 October 2017

  • Softcover ISBN: 978-3-319-88501-8Published: 15 August 2018

  • eBook ISBN: 978-3-319-67873-3Published: 26 September 2017

  • Series ISSN: 2198-4182

  • Series E-ISSN: 2198-4190

  • Edition Number: 1

  • Number of Pages: XIX, 232

  • Number of Illustrations: 24 b/w illustrations

  • Topics: Computational Intelligence, Artificial Intelligence

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