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Semihypergroup Theory

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Semihypergroup Theory

Semihypergroup Theory Book
Author : Bijan Davvaz
Publisher : Academic Press
Release : 2016-06-24
ISBN : 0128099259
Language : En, Es, Fr & De

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Book Description :

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

On Neutrosophic Extended Triplet LA hypergroups and Strong Pure LA semihypergroups Book
Author : Minghao Hu ,Florentin Smarandache,Xiaohong Zhang
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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

Symmetry in Hyperstructure  Neutrosophic Extended Triplet Semihypergroups and Regular Hypergroups Book
Author : Xiaohong Zhang ,Florentin Smarandache,Yingcang Ma
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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

Hypergroup Theory Book
Author : Bijan Davvaz,Violeta Leoreanu-fotea
Publisher : World Scientific
Release : 2021-12-28
ISBN : 9811249407
Language : En, Es, Fr & De

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Book Description :

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

Harmony Search and Nature Inspired Optimization Algorithms Book
Author : Neha Yadav,Anupam Yadav,Jagdish Chand Bansal,Kusum Deep,Joong Hoon Kim
Publisher : Springer
Release : 2018-08-23
ISBN : 981130761X
Language : En, Es, Fr & De

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Book Description :

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

Applications of Artificial Intelligence Techniques in Engineering Book
Author : Hasmat Malik,Smriti Srivastava,Yog Raj Sood,Aamir Ahmad
Publisher : Springer
Release : 2018-09-28
ISBN : 9811318190
Language : En, Es, Fr & De

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Book Description :

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

Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures Book
Author : Jana, Chiranjibe,Senapati, Tapan,Pal, Madhumangal
Publisher : IGI Global
Release : 2019-10-25
ISBN : 1799801926
Language : En, Es, Fr & De

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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.

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures Book
Author : Irina Cristea
Publisher : MDPI
Release : 2020-05-29
ISBN : 3039287087
Language : En, Es, Fr & De

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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.

Applications of Hyperstructure Theory

Applications of Hyperstructure Theory Book
Author : P. Corsini,V. Leoreanu
Publisher : Springer Science & Business Media
Release : 2013-03-09
ISBN : 1475737149
Language : En, Es, Fr & De

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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.

Models and Theories in Social Systems

Models and Theories in Social Systems Book
Author : Cristina Flaut,Šárka Hošková-Mayerová,Daniel Flaut
Publisher : Springer
Release : 2018-10-12
ISBN : 3030000842
Language : En, Es, Fr & De

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Book Description :

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

Refined neutrosophic quadruple  po  hypergroups and their fundamental group Book
Author : M. Al-Tahan,B. Davvaz
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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

Neutrosophic Sets and Systems  Book Series  Vol  27  2019 Book
Author : Florentin Smarandache ,Mohamed Abdel-Basset
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

“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

Neutrosophic Sets and Systems  Vol  27  2019 Book
Author : Florentin Smarandache,Mohamed Abdel-Basset
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

“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

Walk Through Weak Hyperstructures  A  Hv structures Book
Author : Bijan Davvaz,Thomas Vougiouklis
Publisher : World Scientific
Release : 2018-12-11
ISBN : 9813278889
Language : En, Es, Fr & De

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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.

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras Book
Author : Smarandache, Florentin,Al-Tahan, Madeline
Publisher : IGI Global
Release : 2022-04-15
ISBN : 1668434970
Language : En, Es, Fr & De

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Book Description :

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.

Neutrosophic Triplet Non Associative Semihypergroups with Application

Neutrosophic Triplet Non Associative Semihypergroups with Application Book
Author : Muhammad Gulistan ,Shah Nawaz, Nasruddin Hassan
Publisher : Infinite Study
Release : 2022-07-07
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

In this paper, we extended the idea of a neutrosophic triplet set to non-associative semihypergroups and define neutrosophic triplet LA-semihypergroup.We discuss some basic results and properties. At the end, we provide an application of the proposed structure in Football.

New types of Neutrosophic Set Logic Probability Neutrosophic Over Under Off Set Neutrosophic Refined Set and their Extension to Plithogenic Set Logic Probability with Applications

New types of Neutrosophic Set Logic Probability  Neutrosophic Over  Under  Off Set  Neutrosophic Refined Set  and their Extension to Plithogenic Set Logic Probability  with Applications Book
Author : Florentin Smarandache
Publisher : MDPI
Release : 2019-11-27
ISBN : 3039219383
Language : En, Es, Fr & De

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Book Description :

This book contains 37 papers by 73 renowned experts from 13 countries around the world, on following topics: neutrosophic set; neutrosophic rings; neutrosophic quadruple rings; idempotents; neutrosophic extended triplet group; hypergroup; semihypergroup; neutrosophic extended triplet group; neutrosophic extended triplet semihypergroup and hypergroup; neutrosophic offset; uninorm; neutrosophic offuninorm and offnorm; neutrosophic offconorm; implicator; prospector; n-person cooperative game; ordinary single-valued neutrosophic (co)topology; ordinary single-valued neutrosophic subspace; α-level; ordinary single-valued neutrosophic neighborhood system; ordinary single-valued neutrosophic base and subbase; fuzzy numbers; neutrosophic numbers; neutrosophic symmetric scenarios; performance indicators; financial assets; neutrosophic extended triplet group; neutrosophic quadruple numbers; refined neutrosophic numbers; refined neutrosophic quadruple numbers; multigranulation neutrosophic rough set; nondual; two universes; multiattribute group decision making; nonstandard analysis; extended nonstandard analysis; monad; binad; left monad closed to the right; right monad closed to the left; pierced binad; unpierced binad; nonstandard neutrosophic mobinad set; neutrosophic topology; nonstandard neutrosophic topology; visual tracking; neutrosophic weight; objectness; weighted multiple instance learning; neutrosophic triangular norms; residuated lattices; representable neutrosophic t-norms; De Morgan neutrosophic triples; neutrosophic residual implications; infinitely ∨-distributive; probabilistic neutrosophic hesitant fuzzy set; decision-making; Choquet integral; e-marketing; Internet of Things; neutrosophic set; multicriteria decision making techniques; uncertainty modeling; neutrosophic goal programming approach; shale gas water management system.

Polygroup Theory and Related Systems

Polygroup Theory and Related Systems Book
Author : Bijan Davvaz
Publisher : World Scientific
Release : 2012
ISBN : 9814425311
Language : En, Es, Fr & De

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Book Description :

This monograph is devoted to the study of Polygroup Theory. It begins with some basic results concerning group theory and algebraic hyperstructures, which represent the most general algebraic context, in which reality can be modeled. Most results on polygroups are collected in this book. Moreover, this monograph is the first book on this theory. The volume is highly recommended to theoreticians in pure and applied mathematics.

Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets

Algebraic Structures of Neutrosophic Triplets  Neutrosophic Duplets  or Neutrosophic Multisets Book
Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Release : 2019-04-04
ISBN : 3038974757
Language : En, Es, Fr & De

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Book Description :

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor . Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set. This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc.