Fuzzy Algebraic Hyperstructures - Cristea, Irina

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Résumé :
This book is intended as an introduction to fuzzy algebraic hyperstructures. As the first in its genre, it includes a number of topics, most of which reflect the authors? past research and thus provides a starting point for future research directions. The book is organized in five chapters. The first chapter introduces readers to the basic notions of algebraic structures and hyperstructures. The second covers fuzzy sets, fuzzy groups and fuzzy polygroups. The following two chapters are concerned with the theory of fuzzy Hv-structures: while the third chapter presents the concept of fuzzy Hv-subgroup of Hv-groups, the fourth covers the theory of fuzzy Hv-ideals of Hv-rings. The final chapter discusses several connections between hypergroups and fuzzy sets, and includes a study on the association between hypergroupoids and fuzzy sets endowed with two membership functions. In addition to providing a reference guide to researchers, the book is also intended as textbook for undergraduateand graduate students.

Biographie:
Bijan Davvaz is Professor at the Department of Mathematical Sciences, Yazd University, Iran. He also has served as the Head of the Department of Mathematics (1998-2002), Chairman of the Faculty of Science (2004-2006) and Vice-President for Research (2006-2008) at Yazd University, Iran. He earned his PhD in Mathematics with a thesis on Topics in Algebraic Hyperstructures from Tarbiat Modarres University, Iran, and completed his M.Sc. in Mathematics from the University of Tehran, Iran. His areas of interest include algebra, algebraic hyperstructures, rough sets and fuzzy logic. On the editorial boards of 25 mathematical journals, Prof. Davvaz has contributed more than 700 research papers on algebra, fuzzy logic and algebraic hyperstructures. He also has authored eight books including three with Springer: Examples and Problems in Advanced Calculus: Real-Valued Functions, Groups and Symmetry: Theory and Applications and A First Course in Group Theory....

Sommaire:
Fundamentals of Algebraic (Hyper)Structures.- Fuzzy Polygroups.- Fuzzy Hv-Subgroups of Hv-Groups.- Hv-Rings (hyperrings) and Hv-Ideal.- Connections Between Hypergroups And Fuzzy Sets.