Studies in Fuzziness and Soft Computing

Fuzzy Group Theory

Authors: Mordeson, John N., Bhutani, Kiran R., Rosenfeld, A.

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About this book

This book presents an up-to-date account of research in important topics of fuzzy group theory. The book concentrates on the theoretical aspects of fuzzy subgroups of a group. It also includes applications to some abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. The notions of ascending series and descending series of fuzzy subgroups are used to define nilpotency of a fuzzy subgroup. Fuzzy subgroups of Hamiltonian, solvable, P-Hall, and nilpotent groups are discussed. Construction of free fuzzy subgroups is determined. Numerical invariants of fuzzy subgroups of Abelian groups are developed. The problem in group theory of obtaining conditions under which a group can be expressed as a direct product of its normal subgroups is considered. The number of fuzzy subgroups (up to an equivalence relation) of certain finite Abelian groups is determined. Methods for deriving fuzzy theorems from crisp ones are presented and the embedding of lattices of fuzzy subgroups into lattices of crisp groups is discussed. Deriving membership functions from similarity relations is considered.

The material presented in this book makes it a good reference for graduate students and researchers working in fuzzy group theory.

Reviews

From the reviews of the first edition:

"The purpose of this book is to present an up to date account of fuzzy subgroups of a group, it is the first book dedicated entirely to the rapidly growing field of fuzzy group theory. … The book represents a major contribution to the literature on fuzzy groups. It is indispensable for researchers in this field, but also highly suitable as textbook for students at the graduate level." (Xie Xiang-Yun, Zentralblatt MATH, Vol. 1082, 2006)


Table of contents (7 chapters)

  • Fuzzy Subsets and Fuzzy Subgroups

    John N. Mordeson, Kiran R. Bhutani, Azriel Rosenfeld

    Pages 1-39

  • Fuzzy Caley's Theorem and Fuzzy Lagrange's Theorem

    John N. Mordeson, Kiran R. Bhutani, Azriel Rosenfeld

    Pages 41-60

  • Nilpotent, Commutator, and Solvable Fuzzy Subgroups

    John N. Mordeson, Kiran R. Bhutani, Azriel Rosenfeld

    Pages 61-89

  • Characterization of Certain Groups and Fuzzy Subgroups

    John N. Mordeson, Kiran R. Bhutani, Azriel Rosenfeld

    Pages 91-118

  • Fuzzy Subgroups of Abelian Groups

    John N. Mordeson, Kiran R. Bhutani, Azriel Rosenfeld

    Pages 139-166

Buy this book

eBook $189.00
price for USA (gross)
  • ISBN 978-3-540-32395-2
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $239.00
price for USA
  • ISBN 978-3-540-25072-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $239.00
price for USA
  • ISBN 978-3-642-06412-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fuzzy Group Theory
Authors
Series Title
Studies in Fuzziness and Soft Computing
Series Volume
182
Copyright
2005
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-32395-2
DOI
10.1007/b12359
Hardcover ISBN
978-3-540-25072-2
Softcover ISBN
978-3-642-06412-8
Series ISSN
1434-9922
Edition Number
1
Number of Pages
XIV, 300
Topics