© 2015

Fuzzy Algebraic Hyperstructures

An Introduction


  • Makes readers familiar with fundamentals of fuzzy algebraic hyperstructures

  • Presents several connections between hypergroups and fuzzy sets

  • Written by experts in the field


Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 321)

Table of contents

  1. Front Matter
    Pages 1-9
  2. Bijan Davvaz, Irina Cristea
    Pages 1-37
  3. Bijan Davvaz, Irina Cristea
    Pages 39-90
  4. Bijan Davvaz, Irina Cristea
    Pages 91-126
  5. Bijan Davvaz, Irina Cristea
    Pages 127-157
  6. Bijan Davvaz, Irina Cristea
    Pages 159-228
  7. Back Matter
    Pages 229-242

About this book


This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors’ past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduate and graduate students.


Fuzzy Grade of a Hypergroupoid Fuzzy Homomorphisms Fuzzy Hv-structures Fuzzy Hv-submodules Fuzzy Hypergroups Fuzzy Hyperrings Fuzzy Mathematics Fuzzy Subpolygroups Multivalued Systems Probabilistic Fuzzy Semihypergroups

Authors and affiliations

  1. 1.Department of MathematicsYazd UniversityYazdIran
  2. 2.University of Nova Gorica CSITNova GoricaSlovenia

Bibliographic information

  • Book Title Fuzzy Algebraic Hyperstructures
  • Book Subtitle An Introduction
  • Authors Bijan Davvaz
    Irina Cristea
  • Series Title Studies in Fuzziness and Soft Computing
  • Series Abbreviated Title Studies in Fuzziness
  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-319-14761-1
  • Softcover ISBN 978-3-319-38653-9
  • eBook ISBN 978-3-319-14762-8
  • Series ISSN 1434-9922
  • Series E-ISSN 1860-0808
  • Edition Number 1
  • Number of Pages X, 242
  • Number of Illustrations 1 b/w illustrations, 0 illustrations in colour
  • Topics Computational Intelligence
    General Algebraic Systems
    Symbolic and Algebraic Manipulation
  • Buy this book on publisher's site
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“The book is written as an introduction to fuzzy algebraic hyperstructures. … The book could be useful to researchers and students.” (Mirela Ştefănescu, zbMATH 1321.08003, 2015)