Fuzzy Algebraic Hyperstructures An Introduction

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...

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Bibliographic Details
Main Authors: Davvaz, Bijan, Cristea, Irina
Format: eBook Book
Language:English
Published: Cham Springer Nature 2015
Springer
Springer International Publishing AG
Springer International Publishing
Edition:1
Series:Studies in Fuzziness and Soft Computing
Subjects:
Computational Intelligence
Engineering
Engineering & allied operations
Fuzzy logic
Fuzzy sets
General Algebraic Systems
Hypergroups
Symbolic and Algebraic Manipulation
ISBN:9783319147628, 3319147625, 3319147617, 9783319147611
ISSN:1434-9922, 1860-0808
Online Access:Get full text
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Abstract 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 undergraduate and graduate students.
AbstractList 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 undergraduate and graduate students.
Author Davvaz, Bijan
Cristea, Irina
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Snippet 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...
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SubjectTerms Computational Intelligence
Engineering
Engineering & allied operations
Fuzzy logic
Fuzzy sets
General Algebraic Systems
Hypergroups
Symbolic and Algebraic Manipulation
Subtitle An Introduction
TableOfContents Intro -- Preface -- Contents -- Fundamentals of Algebraic (Hyper)Structures -- 1.1 Groups -- 1.2 Rings -- 1.3 Polygroups -- 1.4 Hypergroups -- 1.5 Hyperrings -- 1.6 Hv-Structures -- Fuzzy Polygroups -- 2.1 What Fuzzy Sets Are? -- 2.2 Groups and Fuzzy Subgroups -- 2.3 Polygroups and Fuzzy Subpolygroups -- 2.4 Generalized Fuzzy Subpolygroups -- 2.5 Roughness in Polygroups -- 2.6 F-Polygroups -- Fuzzy Hv-Subgroups of Hv-Groups -- 3.1 Fuzzy Hv-Subgroups and Fuzzy Homomorphisms -- 3.2 Generalized Fuzzy Hv-Subgroups -- 3.3 Intuitionistic Fuzzy Hv-Subgroups -- 3.4 T-Product of Fuzzy Hv-Subgroups -- 3.5 Probabilistic Fuzzy Semihypergroups -- 3.6 F-Hypergroups -- Hv-Rings (Hyperrings) and Hv-Ideals -- 4.1 Fuzzy Hv-Ideals -- 4.2 Generalized Fuzzy Hv-Ideals -- 4.3 Interval-Valued Fuzzy Hv-Ideals -- 4.4 Fuzzy Hyperrings -- Connections between Hypergroups and Fuzzy Sets -- 5.1 Join Spaces and Fuzzy Sets -- 5.1.1 Constructions Using Fuzzy Sets -- 5.1.2 Generalizations to L-Fuzzy Sets -- 5.2 L-Fuzzy Join Spaces -- 5.3 Fuzzy Grade of a Hypergroupoid -- 5.3.1 The Main Construction -- 5.3.2 Intuitionistic Fuzzy Grade of a Hypergroupoid -- 5.3.3 Some Examples: Complete Hypergroups and i.p.s. Hypergroups -- 5.3.4 Extensions to Hypergraphs -- 5.4 Hypergroupoids and Fuzzy Sets Endowed with Two Membership Functions -- Bibliography -- Index
Title Fuzzy Algebraic Hyperstructures
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