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Fuzzy Differential Equations in Various Approaches

  • Luciana Takata Gomes
  • Laécio Carvalho de Barros
  • Barnabas Bede

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Luciana Takata Gomes, Laécio Carvalho de Barros, Barnabas Bede
    Pages 1-10
  3. Luciana Takata Gomes, Laécio Carvalho de Barros, Barnabas Bede
    Pages 11-40
  4. Luciana Takata Gomes, Laécio Carvalho de Barros, Barnabas Bede
    Pages 41-67
  5. Luciana Takata Gomes, Laécio Carvalho de Barros, Barnabas Bede
    Pages 69-113
  6. Back Matter
    Pages 115-120

About this book

Introduction

This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems. Beginning with a historical overview and introduction to fundamental notions of fuzzy sets, including different possibilities of fuzzy differentiation and metric spaces, this book moves on to an overview of fuzzy calculus thorough exposition and comparison of different approaches. Innovative theories of fuzzy calculus and fuzzy differential equations using fuzzy bunches of functions are introduced and explored. Launching with a brief review of essential theories, this book investigates both well-known and novel approaches in this field; such as the Hukuhara differentiability and its generalizations as well as differential inclusions and Zadeh’s extension. Through a unique analysis, results of all these theories are examined and compared.

Keywords

Fuzzy differential equations Hukuhara Derivative SBMAC Zadeh's extension dynamical systems fuzzy-set-valued functions uncertainty analysis

Authors and affiliations

  • Luciana Takata Gomes
    • 1
  • Laécio Carvalho de Barros
    • 2
  • Barnabas Bede
    • 3
  1. 1.Department of Chemistry, Physics and MathematicsUniversity of Sao Carlos Campus SorocabaSorocabaBrazil
  2. 2.Institute of Mathematics, Statistics and Scientific ComputationUniversity of Campinas Department of Applied MathematicsCampinasBrazil
  3. 3.Department of MathematicsDigiPen Institute Of TechnologyRedmondUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-22575-3
  • Copyright Information The Author(s) 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-22574-6
  • Online ISBN 978-3-319-22575-3
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site
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