Fuzzy Algebraic Hyperstructures
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Fuzzy Algebraic Hyperstructures
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Author : Bijan Davvaz
language : en
Publisher: Springer
Release Date : 2015-01-23
Fuzzy Algebraic Hyperstructures written by Bijan Davvaz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-23 with Technology & Engineering categories.
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.
Symmetry In Classical And Fuzzy Algebraic Hypercompositional Structures
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Author : Irina Cristea
language : en
Publisher: MDPI
Release Date : 2020-05-29
Symmetry In Classical And Fuzzy Algebraic Hypercompositional Structures written by Irina Cristea and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-29 with Mathematics categories.
This book is a collection of 12 innovative research papers in the field of hypercompositional algebra, 7 of them being more theoretically oriented, with the other 5 presenting strong applicative aspects in engineering, control theory, artificial intelligence, and graph theory. Hypercompositional algebra is now a well-established branch of abstract algebra dealing with structures endowed with multi-valued operations, also called hyperoperations, having a set as the result of the interrelation between two elements of the support set. The theoretical papers in this book are principally related to three main topics: (semi)hypergroups, hyperfields, and BCK-algebra. Heidari and Cristea present a natural generalization of breakable semigroups, defining the breakable semihypergroups where every non-empty subset is a subsemihypergroup. Using the fundamental relation β on a hypergroup, some new properties of the β-classes are obtained by De Salvo et al., who introduced and investigated the notion of height of a β-class. Based on the properties of a cyclic hypergroup of particular matrices, Krehlik and Vyroubalova describe the symmetry of lower and upper approximations in certain rough sets connected with this hypergroup. These results suggest an application to the study of detection sensors. In the framework of hyperrings and hyperfields theory, a new line of research has been developed regarding hyperhomographies on Krasner hyperfields, with interesting applications in cryptography (Vahedi et al.) and new fuzzy weak hyperideals were defined in Hv-rings by using the concept of fuzzy multiset (Al Tahan et al.), for which some algebraic properties were obtained. Two articles are dedicated to the study of BCK-algebras. Bordbar et al. present the properties of the relative annihilator in lower BCK-semilattices, whereas several types of intuitionistic fuzzy soft ideals in hyper BCK-algebras were defined and studied by Xin et al. Increasing numbers of researchers are interested in the applicative aspects of algebraic hypercompositional structures. For example, new properties related with symmetric relations are emphasized by Chvalina and Smetana for the structures and hyperstructures of artificial neurons. Novak et al. present a mathematical model based on elements of algebraic hyperstructure theory, used in the context of underwater wireless sensor networks. A construction of granular structures using m-polar fuzzy hypergraphs and level hypergraphs is illustrated in Luqman et al. using examples from a real-life problem. In the last paper in this book, Akram et al. discuss some properties related to edge regularity for q-rung picture fuzzy graphs.
Applications Of Hyperstructure Theory
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Author : P. Corsini
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Applications Of Hyperstructure Theory written by P. Corsini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.
Groups And Symmetry
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Author : Bijan Davvaz
language : en
Publisher: Springer Nature
Release Date : 2021-11-17
Groups And Symmetry written by Bijan Davvaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-17 with Mathematics categories.
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. This is the second book of the set of two books on groups theory. Topics on linear transformation and linear groups, group actions on sets, Sylow’s theorem, simple groups, products of groups, normal series, free groups, platonic solids, Frieze and wallpaper symmetry groups and characters of groups have been discussed in depth. Covering all major topics, this book is targeted to advanced undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Walk Through Weak Hyperstructures A Hv Structures
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Author : Bijan Davvaz
language : en
Publisher: World Scientific
Release Date : 2018-12-11
Walk Through Weak Hyperstructures A Hv Structures written by Bijan Davvaz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-11 with Mathematics categories.
Hyperstructures represent a natural extension of classical algebraic structures. They were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers published on this subject. This book is devoted to the study of weak hyperstructures with natural examples. It begins with some basic results, which represent the most general algebraic context, in which reality can be modelled. There are also applications in natural science (Biology, Chemistry and Physics).The authors of the book are experts and well known on this theory. Most results on weak hyperstructures are collected in this book. The overall strength of the book is in its presentation and introduction to some of the results, methods and ideas about weak hyperstructures.
A First Course In Group Theory
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Author : Bijan Davvaz
language : en
Publisher: Springer Nature
Release Date : 2021-11-10
A First Course In Group Theory written by Bijan Davvaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-10 with Mathematics categories.
This textbook provides a readable account of the examples and fundamental results of groups from a theoretical and geometrical point of view. Topics on important examples of groups (like cyclic groups, permutation groups, group of arithmetical functions, matrix groups and linear groups), Lagrange’s theorem, normal subgroups, factor groups, derived subgroup, homomorphism, isomorphism and automorphism of groups have been discussed in depth. Covering all major topics, this book is targeted to undergraduate students of mathematics with no prerequisite knowledge of the discussed topics. Each section ends with a set of worked-out problems and supplementary exercises to challenge the knowledge and ability of the reader.
Handbook Of Research On Emerging Applications Of Fuzzy Algebraic Structures
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Author : Chiranjibe Jana
language : en
Publisher: Engineering Science Reference
Release Date : 2019-10-25
Handbook Of Research On Emerging Applications Of Fuzzy Algebraic Structures written by Chiranjibe Jana and has been published by Engineering Science Reference this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Algebra categories.
"This book examines the use of fuzzy algebraic structures in various applications"--
Vectors And Functions Of Several Variables
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Author : Bijan Davvaz
language : en
Publisher: Springer Nature
Release Date : 2023-07-12
Vectors And Functions Of Several Variables written by Bijan Davvaz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-12 with Mathematics categories.
This comprehensive textbook explores the topics of vector functions and functions of several variables. With over 500 exercises and problems, carefully chosen for their challenging, interesting, and educational value, this book is an ideal resource for undergraduate students of mathematics, statistics, computer science, engineering and the basic sciences. The material is organized into 10 chapters, each of which begins with necessary definitions, concepts and theorems to provide a solid foundation for understanding the topic. In addition, the book includes detailed solutions to all exercises and problems to help students test their understanding and reinforce their learning. Overall, this book is an excellent choice for anyone seeking a thorough introduction to calculus.
Algebraic Hyperstructures And Applications
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Author : Thomas Vougiouklis
language : en
Publisher: World Scientific
Release Date : 1991-04-22
Algebraic Hyperstructures And Applications written by Thomas Vougiouklis and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-22 with categories.
Topics covered include semihypergroups, hypergroups, hyperrings, hyperfields, hypermatrices, ordered hyperstructures etc., related topics as join spaces, cogroups, polygroups and finally applications on combinatorics, field theory, finite geometry, computer science etc. Contents:Themes and Problems of Hypergroup Theory (P Corsini)Sur les Structures Hypercompositionnelles (J Mittas)Sur les Hypercorps et les Hyperanneaux (D Stratigopoulos)Generalized Designs, Linear Spaces, Hypergroupoids and Algebraic Cryptography (L Berardi et al)Some Problems on Hypergroups (S Comer)Hypernear-Rings (V Dasic)Similitude and Isomorphism in KH Hypergroups (M De Salvo)Lexicographic Sums of Ordered Sets and Hypergroupoids (S Foldes)Simplifiable Semihypergroups (C Gutan)On the Hypergroups which can be Defined Over Families of Subsets of a Hypergroup (M Gutan)Reduced Hypergroups (J Jantosciak)Associatively Semihypergroups and Cardinal-Valued Semigroups (T Kepka)and other papers Readership: Pure & applied mathematicians and graduate students in mathematics. keywords:
Algebraic Hyperstructures And Applications
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Author : Piergiulio Corsini
language : en
Publisher:
Release Date : 2004
Algebraic Hyperstructures And Applications written by Piergiulio Corsini and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Ordered algebraic structures categories.
This book is a record of the contents of the papers accepted for publication as the Proceedings of the 7th International Conference on Algebraic Hyperstructures and Applications, held in Taormina (Italy) on June 13-19, 1999.