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Generalized Concavity in Fuzzy Optimization and Decision Analysis

  • Jaroslav Ramík
  • Milan Vlach

Part of the International Series in Operations Research & Management Science book series (ISOR, volume 41)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Theory

    1. Front Matter
      Pages 1-3
    2. Jaroslav Ramík, Milan Vlach
      Pages 5-10
    3. Jaroslav Ramík, Milan Vlach
      Pages 11-36
    4. Jaroslav Ramík, Milan Vlach
      Pages 37-71
    5. Jaroslav Ramík, Milan Vlach
      Pages 73-99
    6. Jaroslav Ramík, Milan Vlach
      Pages 101-119
    7. Jaroslav Ramík, Milan Vlach
      Pages 121-157
  3. Applications

    1. Front Matter
      Pages 159-161
    2. Jaroslav Ramík, Milan Vlach
      Pages 163-191
    3. Jaroslav Ramík, Milan Vlach
      Pages 193-215
    4. Jaroslav Ramík, Milan Vlach
      Pages 217-251
    5. Jaroslav Ramík, Milan Vlach
      Pages 253-282
  4. Back Matter
    Pages 283-296

About this book

Introduction

Convexity of sets in linear spaces, and concavity and convexity of functions, lie at the root of beautiful theoretical results that are at the same time extremely useful in the analysis and solution of optimization problems, including problems of either single objective or multiple objectives. Not all of these results rely necessarily on convexity and concavity; some of the results can guarantee that each local optimum is also a global optimum, giving these methods broader application to a wider class of problems. Hence, the focus of the first part of the book is concerned with several types of generalized convex sets and generalized concave functions. In addition to their applicability to nonconvex optimization, these convex sets and generalized concave functions are used in the book's second part, where decision-making and optimization problems under uncertainty are investigated.
Uncertainty in the problem data often cannot be avoided when dealing with practical problems. Errors occur in real-world data for a host of reasons. However, over the last thirty years, the fuzzy set approach has proved to be useful in these situations. It is this approach to optimization under uncertainty that is extensively used and studied in the second part of this book. Typically, the membership functions of fuzzy sets involved in such problems are neither concave nor convex. They are, however, often quasiconcave or concave in some generalized sense. This opens possibilities for application of results on generalized concavity to fuzzy optimization. Despite this obvious relation, applying the interface of these two areas has been limited to date. It is hoped that the combination of ideas and results from the field of generalized concavity on the one hand and fuzzy optimization on the other hand outlined and discussed in Generalized Concavity in Fuzzy Optimization and Decision Analysis will be of interest to both communities. Our aim is to broaden the classes of problems that the combination of these two areas can satisfactorily address and solve.

Keywords

addition calculus optimization scheduling sets

Authors and affiliations

  • Jaroslav Ramík
    • 1
  • Milan Vlach
    • 2
    • 3
  1. 1.School of Business AdministrationSilesian UniversityKarvináCzech Republic
  2. 2.School of Information ScienceJapan Advanced Institute of Science and TechnologyIshikawaJapan
  3. 3.Faculty of Mathematics and PhysicsCharles UniversityPragueCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-1485-5
  • Copyright Information Kluwer Academic Publishers 2002
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-5577-9
  • Online ISBN 978-1-4615-1485-5
  • Series Print ISSN 0884-8289
  • Buy this book on publisher's site