Semihypergroup Theory Book

Semihypergroup Theory


  • Author : Bijan Davvaz
  • Publisher : Academic Press
  • Release Date : 2016-06-24
  • Genre: Mathematics
  • Pages : 164
  • ISBN 10 : 9780128099254

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Semihypergroup Theory Excerpt :

Semihypergroup Theory is the first book devoted to the semihypergroup theory and it includes basic results concerning semigroup theory and algebraic hyperstructures, which represent the most general algebraic context in which reality can be modelled. Hyperstructures represent a natural extension of classical algebraic structures and they were introduced in 1934 by the French mathematician Marty. Since then, hundreds of papers have been published on this subject. Offers the first book devoted to the semihypergroup theory Presents an introduction to recent progress in the theory of semihypergroups Covers most of the mathematical ideas and techniques required in the study of semihypergroups Employs the notion of fundamental relations to connect semihypergroups to semigroups

On Neutrosophic Extended Triplet LA hypergroups and Strong Pure LA semihypergroups Book

On Neutrosophic Extended Triplet LA hypergroups and Strong Pure LA semihypergroups


  • Author : Minghao Hu
  • Publisher : Infinite Study
  • Release Date : 2022-12-04
  • Genre: Mathematics
  • Pages : 24
  • ISBN 10 : 978186723xxxx

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On Neutrosophic Extended Triplet LA hypergroups and Strong Pure LA semihypergroups Excerpt :

We introduce the notions of neutrosophic extended triplet LA-semihypergroup, neutrosophic extended triplet LA-hypergroup, which can reflect some symmetry of hyperoperation and discuss the relationships among them and regular LA-semihypergroups, LA-hypergroups, regular LA-hypergroups. In particular, we introduce the notion of strong pure neutrosophic extended triplet LA-semihypergroup, get some special properties of it and prove the construction theorem about it under the condition of asymmetry. The examples in this paper are all from Python programs.

Symmetry in Hyperstructure  Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups Book

Symmetry in Hyperstructure Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups


  • Author : Xiaohong Zhang
  • Publisher : Infinite Study
  • Release Date : 2022-12-04
  • Genre: Mathematics
  • Pages : 17
  • ISBN 10 : 978186723xxxx

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Symmetry in Hyperstructure Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups Excerpt :

The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic extended triplet hypergroup (NET-hypergroup) are firstly introduced, some basic properties are obtained, and the relationships among NET- semihypergroups, regular semihypergroups, NET-hypergroups and regular hypergroups are systematically are investigated. Moreover, pure NET-semihypergroup and pure NET-hypergroup are investigated, and a strucuture theorem of commutative pure NET-semihypergroup is established. Finally, a new notion of weak commutative NET-semihypergroup is proposed, some important examples are obtained by software MATLAB, and the following important result is proved: every pure and weak commutative NET-semihypergroup is a disjoint union of some regular hypergroups which are its subhypergroups.

Hypergroup Theory Book

Hypergroup Theory


  • Author : Bijan Davvaz
  • Publisher : World Scientific
  • Release Date : 2021-12-28
  • Genre: Mathematics
  • Pages : 300
  • ISBN 10 : 9789811249402

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Hypergroup Theory Excerpt :

The book presents an updated study of hypergroups, being structured on 12 chapters in starting with the presentation of the basic notions in the domain: semihypergroups, hypergroups, classes of subhypergroups, types of homomorphisms, but also key notions: canonical hypergroups, join spaces and complete hypergroups. A detailed study is dedicated to the connections between hypergroups and binary relations, starting from connections established by Rosenberg and Corsini. Various types of binary relations are highlighted, in particular equivalence relations and the corresponding quotient structures, which enjoy certain properties: commutativity, cyclicity, solvability.A special attention is paid to the fundamental beta relationship, which leads to a group quotient structure. In the finite case, the number of non-isomorphic Rosenberg hypergroups of small orders is mentioned. Also, the study of hypergroups associated with relations is extended to the case of hypergroups associated to n-ary relations. Then follows an applied excursion of hypergroups in important chapters in mathematics: lattices, Pawlak approximation, hypergraphs, topology, with various properties, characterizations, varied and interesting examples. The bibliography presented is an updated one in the field, followed by an index of the notions presented in the book, useful in its study.

Harmony Search and Nature Inspired Optimization Algorithms Book

Harmony Search and Nature Inspired Optimization Algorithms


  • Author : Neha Yadav
  • Publisher : Springer
  • Release Date : 2018-08-23
  • Genre: Technology & Engineering
  • Pages : 1238
  • ISBN 10 : 9789811307614

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Harmony Search and Nature Inspired Optimization Algorithms Excerpt :

The book covers different aspects of real-world applications of optimization algorithms. It provides insights from the Fourth International Conference on Harmony Search, Soft Computing and Applications held at BML Munjal University, Gurgaon, India on February 7–9, 2018. It consists of research articles on novel and newly proposed optimization algorithms; the theoretical study of nature-inspired optimization algorithms; numerically established results of nature-inspired optimization algorithms; and real-world applications of optimization algorithms and synthetic benchmarking of optimization algorithms.

Applications of Artificial Intelligence Techniques in Engineering Book

Applications of Artificial Intelligence Techniques in Engineering


  • Author : Hasmat Malik
  • Publisher : Springer
  • Release Date : 2018-09-28
  • Genre: Technology & Engineering
  • Pages : 643
  • ISBN 10 : 9789811318191

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Applications of Artificial Intelligence Techniques in Engineering Excerpt :

The book is a collection of high-quality, peer-reviewed innovative research papers from the International Conference on Signals, Machines and Automation (SIGMA 2018) held at Netaji Subhas Institute of Technology (NSIT), Delhi, India. The conference offered researchers from academic and industry the opportunity to present their original work and exchange ideas, information, techniques and applications in the field of computational intelligence, artificial intelligence and machine intelligence. The book is divided into two volumes discussing a wide variety of industrial, engineering and scientific applications of the emerging techniques.

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures Book

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures


  • Author : Jana, Chiranjibe
  • Publisher : IGI Global
  • Release Date : 2019-10-25
  • Genre: Mathematics
  • Pages : 439
  • ISBN 10 : 9781799801924

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Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures Excerpt :

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.

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures Book

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures


  • Author : Irina Cristea
  • Publisher : MDPI
  • Release Date : 2020-05-29
  • Genre: Mathematics
  • Pages : 208
  • ISBN 10 : 9783039287086

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Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures Excerpt :

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

Applications of Hyperstructure Theory Book

Applications of Hyperstructure Theory


  • Author : P. Corsini
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-09
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 9781475737141

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Applications of Hyperstructure Theory Excerpt :

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.

Models and Theories in Social Systems Book

Models and Theories in Social Systems


  • Author : Cristina Flaut
  • Publisher : Springer
  • Release Date : 2018-10-12
  • Genre: Technology & Engineering
  • Pages : 576
  • ISBN 10 : 9783030000844

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Models and Theories in Social Systems Excerpt :

This book concisely presents a broad range of models and theories on social systems. Because of the huge spectrum of topics involving social systems, various issues related to Mathematics, Statistics, Teaching, Social Science, and Economics are discussed. In an effort to introduce the subject to a wider audience, this volume, part of the series “Studies in Systems, Decision and Control”, equally addresses the needs of mathematicians, statisticians, sociologists and philosophers. The studies examined here are divided into four parts. The first part, “Perusing the Minds Behind Scientific Discoveries”, traces the winding path of Syamal K. Sen and Ravi P. Agarwal’s scholarship throughout history, and most importantly, the thought processes that allowed each of them to master their subject. The second part covers “Theories in Social Systems” and the third discusses “Models in Social Systems”, while the fourth and final part is dedicated to “Mathematical Methods in the Social Sciences”. Given its breadth of coverage, the book will offer inquisitive readers a valuable point of departure for exploring these rich, vast, and ever-expanding fields of knowledge.

Refined neutrosophic quadruple  po  hypergroups and their fundamental group Book

Refined neutrosophic quadruple po hypergroups and their fundamental group


  • Author : M. Al-Tahan
  • Publisher : Infinite Study
  • Release Date : 2022-12-04
  • Genre: Mathematics
  • Pages : 17
  • ISBN 10 : 978186723xxxx

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Refined neutrosophic quadruple po hypergroups and their fundamental group Excerpt :

After introducing the notion of hyperstructures about 80 years ago by F. Marty, a number of researches on its theory, generalization, and it’s applications have been done. On the other hand, the theory of Neutrosophy, the study of neutralities, was developed in 1995 by F. Smarandache as an extension of dialectics. This paper aims at finding a connection between refined neutrosophy of sets and hypergroups. In this regard, we define refined neutrosophic quadruple hypergroups, study their properties, and find their fundamental refined neutrosophic quadruple

Neutrosophic Sets and Systems  Book Series  Vol  27  2019 Book

Neutrosophic Sets and Systems Book Series Vol 27 2019


  • Author : Florentin Smarandache
  • Publisher : Infinite Study
  • Release Date : 2022-12-04
  • Genre: Mathematics
  • Pages : 252
  • ISBN 10 : 978186723xxxx

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Neutrosophic Sets and Systems Book Series Vol 27 2019 Excerpt :

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

Neutrosophic Sets and Systems  Vol  27  2019 Book

Neutrosophic Sets and Systems Vol 27 2019


  • Author : Florentin Smarandache
  • Publisher : Infinite Study
  • Release Date : 2022-12-04
  • Genre: Mathematics
  • Pages : 252
  • ISBN 10 : 978186723xxxx

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Neutrosophic Sets and Systems Vol 27 2019 Excerpt :

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles from this issue: BMBJ-neutrosophic ideals in BCK/BCI-algebras, Neutrosophic General Finite Automata, Generalized Neutrosophic Exponential map, Implementation of Neutrosophic Function Memberships Using MATLAB Program.

Walk Through Weak Hyperstructures  A  Hv structures Book

Walk Through Weak Hyperstructures A Hv structures


  • Author : Bijan Davvaz
  • Publisher : World Scientific
  • Release Date : 2018-12-11
  • Genre: Mathematics
  • Pages : 348
  • ISBN 10 : 9789813278882

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Walk Through Weak Hyperstructures A Hv structures Excerpt :

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.

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras Book

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras


  • Author : Smarandache, Florentin
  • Publisher : IGI Global
  • Release Date : 2022-04-15
  • Genre: Mathematics
  • Pages : 333
  • ISBN 10 : 9781668434970

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Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras Excerpt :

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities as well as their interactions with different ideational spectra. In all classical algebraic structures, the law of compositions on a given set are well-defined, but this is a restrictive case because there are situations in science where a law of composition defined on a set may be only partially defined and partially undefined, which we call NeutroDefined, or totally undefined, which we call AntiDefined. Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebra introduces NeutroAlgebra, an emerging field of research. This book provides a comprehensive collection of original work related to NeutroAlgebra and covers topics such as image retrieval, mathematical morphology, and NeutroAlgebraic structure. It is an essential resource for philosophers, mathematicians, researchers, educators and students of higher education, and academicians.