Fuzzy Group Theory
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Beschreibung
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.
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.
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
Autor*in
John N. Mordeson
Themen in »Fuzzy Group Theory«
Abelian group Abtract Recognition Problems Fuzzy Fuzzy Group Theory Fuzzy Groups Fuzzy Semigroups Group theory coding theory cognition construction linear optimization complexity
Stimmen zu »Fuzzy Group Theory«
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)
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