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168Neutro-BCK-AlgebraInternational Journal of Neutrosophic Science 8 (2): 110-117. 2020.This paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate.
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79In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.
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124Linguistic Geometry and its ApplicationsGlobal Knowledge. 2022.The notion of linguistic geometry is defined in this book. It is pertinent to keep in the record that linguistic geometry differs from classical geometry. Many basic or fundamental concepts and notions of classical geometry are not true or extendable in the case of linguistic geometry. Hence, for simple illustration, facts like two distinct points in classical geometry always define a line passing through them; this is generally not true in linguistic geometry. Suppose we have two linguistic poi…Read more
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100SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 1Educational Publisher. 2014.In this book the authors introduced the notions of soft neutrosophic algebraic structures. These soft neutrosophic algebraic structures are basically defined over the neutrosophic algebraic structures which means a parameterized collection of subsets of the neutrosophic algebraic structure. For instance, the existence of a soft neutrosophic group over a neutrosophic group or a soft neutrosophic semigroup over a neutrosophic semigroup, or a soft neutrosophic field over a neutrosophic field, or a …Read more
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57The Encyclopedia of Neutrosophic Researchers, 2nd volumeNeutrosophic Science International Association. 2018.This is the second volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to my invitation. The introduction contains a short history of neutrosophics, together with links to the main papers and books.
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83The Encyclopedia of Neutrosophic Researchers, 3rd volumeNeutrosophic Science International Association. 2019.This is the third volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books.
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Supermodular LatticesEducational Publisher. 2012.In lattice theory the two well known equational class of lattices are the distributive lattices and the modular lattices. All distributive lattices are modular however a modular lattice in general is not distributive. In this book, new classes of lattices called supermodular lattices and semi-supermodular lattices are introduced and characterized.
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92Superbimatrices and Their GeneralizationsCuArt. 2009.The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers.
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120Algebraic Structures using Super Interval MatricesEducational Publisher. 2011.In this book authors for the first time introduce the notion of super interval matrices using special intervals. The advantage of using super interval matrices is that one can build only one vector space using m × n interval matrices, but in case of super interval matrices we can have several such spaces depending on the partition on the interval matrix.
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113Superluminal and Instantaneous PhysicsEducational Publisher. 2014.This book is a selection from the papers of the First International Conference on Superluminal Physics as New Fields of Research held at the University of New Mexico, Gallup Campus, USA, in July 2012. The editor have selected seven papers proposed by the following authors and co co-authors Kaizhe Guo Guo, Chongwu Guo Guo, Chen Jianguojianguo, Dong Jingfeng Jingfeng, Mi Haijiang Haijiang, Changwei Hu Hu, Yang Shijiashijia, Guli, and Fu Yuhua Yuhua.
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224The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government.
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111NeutroAlgebra of Neutrosophic Triplets using {Zn, x}Neutrosophic Sets and Systems 38 (1): 509-523. 2020.Smarandache in 2019 has generalized the algebraic structures to NeutroAlgebraic structures and AntiAlgebraic structures. In this paper, authors, for the first time, define the NeutroAlgebra of neutrosophic triplets group under usual+ and x, built using {Zn, x}, n a composite number, 5 < n < oo, which are not partial algebras. As idempotents in Zn alone are neutrals that contribute to neutrosophic triplets groups, we analyze them and build NeutroAlgebra of idempotents under usual + and x, which a…Read more
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77NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries (revisited)Neutrosophic Sets and Systems 46 (1): 456-477. 2021.In this paper we extend the NeutroAlgebra & AntiAlgebra to the geometric spaces, by founding the NeutroGeometry & AntiGeometry.
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71Generalizations and Alternatives of Classical Algebraic Structures to NeutroAlgebraic Structures and AntiAlgebraic StructuresJournal of Fuzzy Extension and Applications 1 (2): 85-87. 2020.In this paper we present the development from paradoxism to neutrosophy, which gave birth to neutrosophic set and logic and especially to NeutroAlgebraic Structures (or NeutroAlgebras) and AntiAlgebraic Structures (or AntiAlgebras) that are generalizations and alternatives of the classical algebraic structures.
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110Linguistic Semilinear Algebras and Linguistic Semivector SpacesGlobal Knowledge. 2022.Algebraic structures on linguistic sets associated with a linguistic variable are introduced. The linguistics with single closed binary operations are only semigroups and monoids. We describe the new notion of linguistic semirings, linguistic semifields, linguistic semivector spaces and linguistic semilinear algebras defined over linguistic semifields. We also define algebraic structures on linguistic subsets of a linguistic set associated with a linguistic variable. We define the notion of ling…Read more
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94SOFT NEUTROSOPHIC ALGEBRAIC STRUCTURES AND THEIR GENERALIZATION, Vol. 2Educational Publisher. 2014.In this book we define some new notions of soft neutrosophic algebraic structures over neutrosophic algebraic structures. We define some different soft neutrosophic algebraic structures but the main motivation is two-fold. Firstly the classes of soft neutrosophic group ring and soft neutrosophic semigroup ring defined in this book is basically the generalization of two classes of rings: neutrosophic group rings and neutrosophic semigroup rings. These soft neutrosophic group rings and soft neutro…Read more
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69The Encyclopedia of Neutrosophic Researchers, 1st volumeNeutrosophic Science International Association. 2016.This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The 78 authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining signif…Read more
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114The Encyclopedia of Neutrosophic Researchers, 4th volumeNeutrosophic Science International Association. 2021.Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial de su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Conjunto neutrosófico, lógica neutrosófica, probabilidad neutrosófica, estadística neutrosófica, medida neutrosófic…Read more
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87Introduction to Neutrosophic GeneticsInternational Journal of Neutrosophic Science 1 (1): 1-5. 2021.Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measure and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mut…Read more
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152Super Linear AlgebraProQuest Information & Learning. 2008.In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a parad…Read more
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57Structure, NeutroStructure, and AntiStructure in ScienceInternational Journal of Neutrosophic Science 13 (1): 28-33. 2021.In any science, a classical Theorem, defined on a given space, is a statement that is 100% true (i.e. true for all elements of the space). To prove that a classical theorem is false, it is sufficient to get a single counter-example where the statement is false.
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106NeutroOrderedAlgebra: Applications to SemigroupsNeutrosophic Sets and Systems 39 (1): 133-147. 2021.Starting with a partial order on a NeutroAlgebra, we get a NeutroStructure. The latter if it satisfies the conditions of NeutroOrder, it becomes a NeutroOrderedAlgebra. In this paper, we apply our new defined notion to semigroups by studying NeutroOrderedSemigroups. More precisely, we define some related terms like NeutrosOrderedSemigroup, NeutroOrderedIdeal, NeutroOrderedFilter, NeutroOrderedHomomorphism, etc., illustrate them via some examples, and study some of their properties.
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285The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumer…Read more
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80The Encyclopedia of Neutrosophic Researchers. Volume IVNeutrosophic Science International Association. 2021.This is the fourth volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining signific…Read more
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249The Encyclopedia of Neutrosophic Researchers. Volume INeutrosophic Science International Association. 2016.This is the first volume of the Encyclopedia of Neutrosophic Researchers, edited from materials offered by the authors who responded to the editor’s invitation. The authors are listed alphabetically. The introduction contains a short history of neutrosophics, together with links to the main papers and books. Neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics, neutrosophic measure, neutrosophic precalculus, neutrosophic calculus and so on are gaining signific…Read more
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98A New Trend to Extensions of CI-algebrasInternational Journal of Neutrosophic Science 5 (1): 8-15. 2020.In this paper, as an extension of CI-algebras, we discuss the new notions of Neutro-CI-algebras and Anti-CI-algebras. First, some examples are given to show that these definitions are different. We prove that any proper CI-algebra is a Neutro-BE-algebra or Anti-BE-algebra. Also, we show that any NeutroSelf-distributive and Anti-Commutative CI-algebras are not BE-algebras.
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100Applications of (Neutro/Anti)sophications to SemihypergroupsJournal of Mathematics 2021 (1): 1-7. 2021.A hypergroup, as a generalization of the notion of a group, was introduced by F. Marty in 1934. The first book in hypergroup theory was published by Corsini. Nowadays, hypergroups have found applications to many subjects of pure and applied mathematics, for example, in geometry, topology, cryptography and coding theory, graphs and hypergraphs, probability theory, binary relations, theory of fuzzy and rough sets and automata theory, physics, and also in biological inheritance.
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59Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures (revisited)Neutrosophic Sets and Systems 31 (1): 1-16. 2020.In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.
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131NeutroAlgebra Theory, volume IEducational Publisher. 2021.Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough ne…Read more
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89DSm Super Vector Space of Refined LabelsZip Publishing. 2011.In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m × n matrix of refined labels are introduced and studied.
Kishinev University
Alumnus, 1997
Areas of Specialization
Science, Logic, and Mathematics |
Areas of Interest
Science, Logic, and Mathematics |
Other Academic Areas |