Reduction of the Pareto Set

An Axiomatic Approach

  • Vladimir D. Noghin

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

Table of contents

  1. Front Matter
    Pages i-xix
  2. Vladimir D. Noghin
    Pages 1-22
  3. Vladimir D. Noghin
    Pages 139-149
  4. Vladimir D. Noghin
    Pages 151-178
  5. Back Matter
    Pages 223-232

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.


Decision-making with Several Numerical Criteria Multicriteria Problems Pareto Sets Fuzzy Information Edgeworth-Pareto Principle

Authors and affiliations

  • Vladimir D. Noghin
    • 1
  1. 1.Department of Control TheorySaint Petersburg State UniversitySaint PetersburgRussia

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-67872-6
  • Online ISBN 978-3-319-67873-3
  • Series Print ISSN 2198-4182
  • Series Online ISSN 2198-4190
  • Buy this book on publisher's site
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