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.
Reviews / Votes
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)
Series
Edition
Softcover reprint of hardcover 1st ed. 2005
Language
Place of publication
Publishing group
Target group
Professional and scholarly
Research
Illustrations
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 18 mm
Weight
ISBN-13
978-3-642-06412-8 (9783642064128)
DOI
Schweitzer Classification
Dr. John N. Mordeson is Professor Emeritus of Mathematics at Creighton University. He received his B.S., M.S., and Ph.D. from Iowa State University. He is a Member of Phi Kappa Phi. He is a President of the Society for Mathematics of Uncertainty. He has published ¿fteen books and two hundred journal articles. He is on the editorial board of numerous journals. He has served as an external examiner of Ph.D. candidates from India, South Africa, Bulgaria, and Pakistan. He has refereed for numerous journals and granting agencies. He is particularly interested in applying mathematics of uncertainty to combat the problem of human traf¿cking.
Dr. Sunil Mathew is currently a Faculty Member in the Department of Mathematics, NIT Calicut, India. He has acquired his masters from St. Joseph's College Devagiri, Calicut, and Ph.D. from National Institute of Technology Calicut in the area of Fuzzy Graph Theory. He has published more than seventy-¿ve research papers and written two books. He is a Member of several academic bodies and associations. He is editor and reviewer of several international journals. He has an experience of twenty years in teaching and research. His current research topics include fuzzy graph theory, bio-computational modeling, graph theory, fractal geometry, and chaos.
Dr. Davender S. Malik is a Professor of Mathematics at Creighton University. He received his Ph.D. from Ohio University and has published more than ¿fty-¿ve papers and eighteen books on abstract algebra, applied mathematics, graph theory, fuzzy automata theory and languages, fuzzy logic and its applications, programming, data structures, and discrete mathematics.
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.
