A Rosenfeld - Böcker

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.

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.

This book results from a Workshop on Multiresolution Image Processing and Analysis, held in Leesburg, VA on July 19-21, 1982. It contains updated ver­ sions of most of the papers that were presented at the Workshop, as well as new material added by the authors. Four of the presented papers were not available for inclusion in the book: D. Sabbah, A computing with connections approach to visual recognition; R. M. Haralick, Fitting the gray tone intensity surface as a function of neighborhood size; E. M. Riseman, Hierarchical boundary formation; and W. L. Mahaffey, L. S. Davis, and J. K. Aggarwal, Region correspondence in multi-resolution images taken from dynamic scenes. The number and variety of papers indicates the timeliness of the H0rkshop. Multiresolution methods are rapidly gaining recognition as an important theme in image processing and analysis. I would like to express my thanks to the National Science Foundation for their support of the Workshop under Grant MCS-82-05942; to Barbara Hope for organizing and administering the Workshop; to Janet Salzman and Fran Cohen, for retyping the papers; and above all, to the speakers and other partici­ pants, for making the Workshop possible.