Author: Bijan Davvaz
Publisher: Springer
ISBN: 3319147625
Category : Technology & Engineering
Languages : en
Pages : 250

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Book Description
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: Irina Cristea
Publisher: MDPI
ISBN: 3039287087
Category : Mathematics
Languages : en
Pages : 208

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Book Description
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.

Author: P. Corsini
Publisher: Springer Science & Business Media
ISBN: 1475737149
Category : Mathematics
Languages : en
Pages : 333

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Book Description
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.

Author: Jana, Chiranjibe
Publisher: IGI Global
ISBN: 1799801926
Category : Mathematics
Languages : en
Pages : 439

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Book Description
In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices.

Author: Broumi Said
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 94

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Book Description
International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

Author: Panackal Harikrishnan
Publisher: World Scientific
ISBN: 981320737X
Category : Mathematics
Languages : en
Pages : 324

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Book Description
Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology. One of the best tools to study the non-linear algebraic systems is the theory of Near-rings.The forward note by G

Author: Piergiulio Corsini
Publisher:
ISBN:
Category : Ordered algebraic structures
Languages : en
Pages : 160

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Book Description
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.

Author: Sudhakar Radhakrishnan
Publisher: BoD – Books on Demand
ISBN: 1839694092
Category : Computers
Languages : en
Pages : 142

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Book Description
This book explores the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavors. It consists of seven chapters that address such topics as applications of coding theory in networking and cryptography, wireless sensor nodes in wireless body area networks, the construction of linear codes, and more.

Author: Thomas Vougiouklis
Publisher: World Scientific
ISBN: 9814569453
Category :
Languages : en
Pages : 236

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Book Description
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:

Author: Bijan Davvaz
Publisher: World Scientific
ISBN: 9813278889
Category : Mathematics
Languages : en
Pages : 347

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Book Description
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.