On Neutro-BE-algebras and Anti-BE-algebras (revisited)

On Neutro-BE-algebras and Anti-BE-algebras (revisited)
Author: Akbar Rezaei
Publisher: Infinite Study
Total Pages: 8
Release: 2020-05-15
Genre: Antiques & Collectibles
ISBN:
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In this paper, the concepts of Neutro-BE-algebra and Anti-BE-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-BE-algebra and Anti-BE-algebras are alternatives of the class of BE-algebras.

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras

Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras
Author: Smarandache, Florentin
Publisher: IGI Global
Total Pages: 333
Release: 2022-04-15
Genre: Mathematics
ISBN: 1668434970
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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.

On Neutro-𝑩𝑬-algebras and Anti-𝑩𝑬-algebras

On Neutro-𝑩𝑬-algebras and Anti-𝑩𝑬-algebras
Author: Akbar Rezaei
Publisher: Infinite Study
Total Pages: 8
Release:
Genre: Mathematics
ISBN:
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In this paper, the concepts of Neutro-𝐵𝐸-algebra and Anti-𝐵𝐸-algebra are introduced, and some related properties and four theorems are investigated. We show that the classes of Neutro-𝐵𝐸-algebra and Anti-𝐵𝐸-algebras are alternatives of the class of 𝐵𝐸-algebras.

Collected Papers. Volume IX

Collected Papers. Volume IX
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 1008
Release: 2022-05-10
Genre: Mathematics
ISBN:
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This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang.

NeutroAlgebra Theory Volume I

NeutroAlgebra Theory Volume I
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 219
Release: 2021-06-21
Genre: Architecture
ISBN:
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A collection of papers from multiple authors. In 2019 and 2020 Smarandache [1, 2, 3, 4] generalized the classical Algebraic Structures to NeutroAlgebraic Structures (or NeutroAlgebras) {whose operations and axioms are partially true, partially indeterminate, and partially false} as extensions of Partial Algebra, and to AntiAlgebraic Structures (or AntiAlgebras) {whose operations and axioms are totally false}. The NeutroAlgebras & AntiAlgebras are a new field of research, which is inspired from our real world. In classical algebraic structures, all axioms are 100%, and all operations are 100% well-defined, but in real life, in many cases these restrictions are too harsh, since in our world we have things that only partially verify some laws or some operations. Using the process of NeutroSophication of a classical algebraic structure we produce a NeutroAlgebra, while the process of AntiSophication of a classical algebraic structure produces an AntiAlgebra.

Neutrosophic Sets and Systems, vol. 51/2022

Neutrosophic Sets and Systems, vol. 51/2022
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 970
Release: 2022-09-01
Genre: Mathematics
ISBN:
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“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. 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. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).

NeutroVectorSpaces I

NeutroVectorSpaces I
Author: M.A. Ibrahim
Publisher: Infinite Study
Total Pages: 23
Release: 2020-10-01
Genre: Mathematics
ISBN:
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Recently, the concept of NeutroAlgebraic and AntiAlgebraic Structures were introduced and analyzed by Florentin Smarandache. His new approach to the study of Neutrosophic Structures presents a more robust tool needed for managing uncertainty, incompleteness, indeterminate and imprecise information. In this paper, we introduce for the first time the concept of NeutroVector Spaces. Specifically, we study a particular class of the NeutroVectorSpaces called of type 4S and their elementarily properties are presented. It is shown that the NeutroVectorSpaces of type 4S may contain NeutroSubspaces of other types and that the intersections of NeutroSubspaces of type 4S are not NeutroSubspaces. Also, it is shown that if NV is a NeutroVector Space of a particular type and NW is a NeutroSubspace of NV , the NeutroQuotientSpace NV=NW does not necessarily belong to the same type as NV .

The Neutrosophic Triplet of BI-algebras

The Neutrosophic Triplet of BI-algebras
Author: Akbar Rezaei
Publisher: Infinite Study
Total Pages: 9
Release: 2020-10-01
Genre: Mathematics
ISBN:
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In this paper, the concepts of a Neutro-𝐵𝐼-algebra and Anti-𝐵𝐼-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-𝐵𝐼-algebra is an alternative of the class of 𝐵𝐼-algebras.

The Neutrosophic Triplet of 𝑩𝑰-algebras

The Neutrosophic Triplet of 𝑩𝑰-algebras
Author: Akbar Rezaei
Publisher: Infinite Study
Total Pages: 9
Release: 2020-05-12
Genre: Antiques & Collectibles
ISBN:
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In this paper, the concepts of a Neutro-𝐵𝐼-algebra and Anti-𝐵𝐼-algebra are introduced, and some related properties are investigated. We show that the class of Neutro-𝐵𝐼-algebra is an alternative of the class of 𝐵𝐼-algebras.

Neutrosophic Sets and Systems, Vol. 38, 2020

Neutrosophic Sets and Systems, Vol. 38, 2020
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 662
Release:
Genre: Mathematics
ISBN:
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“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.