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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.
List of contents
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.
Summary
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.
Additional text
“The book is written as an introduction to fuzzy
algebraic hyperstructures. … The book could be useful to researchers and
students.” (Mirela Ştefănescu, zbMATH 1321.08003, 2015)
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"The book is written as an introduction to fuzzy algebraic hyperstructures. ... The book could be useful to researchers and students." (Mirela Stefanescu, zbMATH 1321.08003, 2015)
