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

Fuzzy Group Theory

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Studies in Fuzziness and Soft Computing 182
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-06412-8
• Softcover reprint of hardcover 1st ed. 2005
• Seitenzahl: 316
• Erscheinungstermin: 21. Oktober 2010
• Englisch
• Abmessung: 235mm x 155mm x 18mm
• Gewicht: 598g
• ISBN-13: 9783642064128
• ISBN-10: 3642064124
• Artikelnr.: 32056423

Inhaltsangabe

Fuzzy Subsets and Fuzzy Subgroups.- Fuzzy Caley's Theorem and Fuzzy Lagrange's Theorem.- Nilpotent, Commutator, and Solvable Fuzzy Subgroups.- Characterization of Certain Groups and Fuzzy Subgroups.- Free Fuzzy Subgroups and Fuzzy Subgroup Presentations.- Fuzzy Subgroups of Abelian Groups.- Direct Products of Fuzzy Subgroups and Fuzzy Cyclic Subgroups.- Equivalence of Fuzzy Subgroups of Finite Abelian Groups.- Lattices of Fuzzy Subgroups.- Membership Functions From Similarity Relations.

Rezensionen

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)