Overview
- Up-to-date account of research in important topics of fuzzy group theory
- Concentrates on the theoretical aspects of fuzzy subgroups of a group
- Good reference for graduate students and researchers working in fuzzy group theory
Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 182)
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About this book
This book presents an up-to-date account of research in important topics of fuzzy group theory. It concentrates on the theoretical aspects of fuzzy subgroups of a group. It includes applications to abstract recognition problems and to coding theory. The book begins with basic properties of fuzzy subgroups. 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. 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 as well as deriving membership functions from similarity relations. The material presented makes this book a good reference for graduate students and researchers working in fuzzy group theory.
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Keywords
Table of contents (10 chapters)
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Front Matter
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Back Matter
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)
Bibliographic Information
Book Title: Fuzzy Group Theory
Authors: John Mordeson, Kiran Bhutani, Azriel Rosenfeld
Series Title: Studies in Fuzziness and Soft Computing
DOI: https://doi.org/10.1007/b12359
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2005
Hardcover ISBN: 978-3-540-25072-2Published: 22 June 2005
Softcover ISBN: 978-3-642-06412-8Published: 21 October 2010
eBook ISBN: 978-3-540-32395-2Published: 22 September 2005
Series ISSN: 1434-9922
Series E-ISSN: 1860-0808
Edition Number: 1
Number of Pages: XIV, 300
Topics: Theory of Computation, Complexity, Artificial Intelligence, Group Theory and Generalizations