Algebraic Structures Of Neutrosophic Triplets Neutrosophic Duplets Or Neutrosophic Multisets

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Page : 478 pages
File Size : 44,7 Mb
Release : 2019-04-04
Category : Mathematics
ISBN : 9783038973843

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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.

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : Infinite Study
Page : 450 pages
File Size : 41,9 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 9783038974765

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume II by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on 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, and several papers have been published in first rank international journals.

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : Infinite Study
Page : 480 pages
File Size : 55,5 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 9783038973850

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets, Volume I by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on 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, and several papers have been published in first rank international journals.

Author : Florentin Smarandache,Xiaohong Zhang (Professor of mathematics),Mumtaz Ali (Research scholar)
Publisher : Unknown
Page : 128 pages
File Size : 48,9 Mb
Release : 2019
Category : Neutrosophic logic
ISBN : 3038974773

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets by Florentin Smarandache,Xiaohong Zhang (Professor of mathematics),Mumtaz Ali (Research scholar) Pdf

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 128 pages
File Size : 51,8 Mb
Release : 2024-06-03
Category : Electronic
ISBN : 9781599735313

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Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications. (2nd edition) by Florentin Smarandache Pdf

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. This is the second extended and improved edition of Neutrosophic Perspectives (September 2017; first edition was published in June 2017). For the first time, we now introduce: — Neutrosophic Duplets and the Neutrosophic Duplet Structures; — Neutrosophic Multisets (as an extension of the classical multisets); — Neutrosophic Spherical Numbers; — Neutrosophic Overnumbers / Undernumbers / Offnumbers; — Neutrosophic Indeterminacy of Second Type; — Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations); — Neutrosophic Triplet Weak Set (and con-sequently we have renamed the previous Neutros-ophic Triplet Set (2014-2016) as Neutrosophic Triplet Strong Set in order to distinguish them); — Neutrosophic Perfect Triplet; — Neutrosophic Imperfect Triplet; — Neutrosophic triplet relation of equivalence; — Two Neutrosophic Friends; — n Neutrosophic Friends; — Neutrosophic Triplet Loop; — Neutrosophic Triplet Function; — Neutrosophic Modal Logic; — and Neutrosophic Hedge Algebras. The Refined Neutrosophic Set / Logic / Probability were introduced in 2013 by F. Smarandache. Since year 2016 a new interest has been manifested by researchers for the Neutrosophic Triplets and their corresponding Neutros-ophic Triplet Algebraic Structures (introduced by F. Smarandache & M. Ali). Subtraction and Division of Neutrosophic Numbers were introduced by F. Smarandache - 2016, and Jun Ye – 2017. We also present various new applications in: neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function (the equatorial virtual line), neutrosophic probability in target identification, neutrosophic dynamic systems, neutrosophic quantum computers, neutrosophic theory of evolution, and neutrosophic triplet structures in our everyday life. Keywords: neutrosophy, neutrosophic duplets, neutrosophic duplet structures, neutrosophic multisets, neutrosophic hedge algebras, neutrosophic multi-criteria decision-making, neutrosophic psychology, neutrosophic geographical function, neutrosophic probability in target identification,

Author : Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali
Publisher : MDPI
Page : 450 pages
File Size : 48,8 Mb
Release : 2019-04-04
Category : Mathematics
ISBN : 9783038974758

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Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets by Florentin Smarandache,Xiaohong Zhang,Mumtaz Ali Pdf

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.

Author : Vasantha Kandasamy,Ilanthenral Kandasamy ,Florentin Smarandache
Publisher : Infinite Study
Page : 14 pages
File Size : 44,8 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Quadruple Algebraic Codes over Z2 and their Properties by Vasantha Kandasamy,Ilanthenral Kandasamy ,Florentin Smarandache Pdf

In this paper we for the rst time develop, de ne and describe a new class of algebraic codes using Neutrosophic Quadruples which uses the notion of known value, and three unknown triplets (T; I; F) where T is the truth value, I is the indeterminate and F is the false value.

Author : Florentin Smarandache,Mohamed Abdel-Basset
Publisher : Infinite Study
Page : 353 pages
File Size : 45,8 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Sets and Systems, Vol. 33, 2020 by Florentin Smarandache,Mohamed Abdel-Basset Pdf

“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 in this issue: Extension of HyperGraph to n-SuperHyperGraph and to Plithogenic n-SuperHyperGraph, and Extension of HyperAlgebra to n-ary (Classical-/Neutro-/Anti-)HyperAlgebra, Neutrosophic Triplet Partial Bipolar Metric Spaces, The Neutrosophic Triplet of BI-algebras.

Author : Florentin Smarandache,Mohamed Abdel-Basset
Publisher : Infinite Study
Page : 341 pages
File Size : 53,6 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Sets and Systems, Book Series, Vol. 33, 2020. An International Book Series in Information Science and Engineering by Florentin Smarandache,Mohamed Abdel-Basset Pdf

Contributors to current issue (listed in papers’ order): Atena Tahmasbpour Meikola, Arif Mehmood, Wadood Ullah, Said Broumi, Muhammad Imran Khan, Humera Qureshi, Muhammad Ibrar Abbas, Humaira Kalsoom, Fawad Nadeem, T. Chalapathi, L. Madhavi, R. Suresh, S. Palaniammal, Nivetha Martin, Florentin Smarandache, S. A. Edalatpanah, Rafif Alhabib, A. A. Salama, Memet Şahin, Abdullah Kargın, Murat Yücel, Dimacha Dwibrang Mwchahary, Bhimraj Basumatary, R. S. Alghamdi, N. O. Alshehri, Shigui Du, Rui Yong, Jun Ye, Vasantha Kandasamy, Ilanthenral Kandasamy, Muhammad Saeed, Muhammad Saqlain, Asad Mehmood, Khushbakht Naseer, Sonia Yaqoob, Sudipta Gayen, Sripati Jha, Manoranjan Kumar Singh, Ranjan Kumar, Huseyin Kamaci, Shawkat Alkhazaleh, Anas Al-Masarwah, Abd Ghafur Ahmad, Merve Sena Uz, Akbar Rezaei, Mohamed Grida, Rehab Mohamed, Abdelnaser H. Zaid.

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 1008 pages
File Size : 44,5 Mb
Release : 2022-05-10
Category : Mathematics
ISBN : 8210379456XXX

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Collected Papers. Volume IX by Florentin Smarandache Pdf

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.

Author : S. Suryoto,Harjito,T. Udjiani
Publisher : Infinite Study
Page : 7 pages
File Size : 48,9 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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The algebraic structure on the neutrosophic triplet set by S. Suryoto,Harjito,T. Udjiani Pdf

The notion of the neutrosophic triplet was introduced by Smarandache and Ali. This notion is based on the fundamental law of neutrosophy that for an idea X, we have neutral of X denoted as neut(X) and anti of X denoted as anti(X). This paper studied a neutrosophic triplet set which is a collection of all triple of three elements that satisfy certain properties with some binary operation. Also given some interesting properties related to them. Further, in this paper investigated that from the neutrosophic triplet group can construct a classical group under multiplicative operation for ℤ𝑛 , for some specific n. These neutrosophic triplet groups are built using only modulo integer 2p, with p is an odd prime or Cayley table.

Author : Vasantha Kandasamy,Ilantheral Kandasamy,Florentin Smarandache
Publisher : Infinite Study
Page : 15 pages
File Size : 44,8 Mb
Release : 2020-12-01
Category : Mathematics
ISBN : 8210379456XXX

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NeutroAlgebra of Neutrosophic Triplets by Vasantha Kandasamy,Ilantheral Kandasamy,Florentin Smarandache Pdf

In this paper, authors define the NeutroAlgebra of neutrosophic triplets groups. We prove the existence theorem for NeutroAlgebra of neutrosophic triplet groups. Several open problems are proposed. Further, the NeutroAlgebras of extended neutrosophic triplet groups have been obtained.

Author : Vasantha Kandasamy W. B. ,Ilanthenral Kandasamy ,Florentin Smarandache
Publisher : Infinite Study
Page : 9 pages
File Size : 44,9 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Triplets in Neutrosophic Rings by Vasantha Kandasamy W. B. ,Ilanthenral Kandasamy ,Florentin Smarandache Pdf

It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.

Author : Vasantha Kandasamy W.B. ,Ilanthenral Kandasamy ,Florentin Smarandache
Publisher : Infinite Study
Page : 8 pages
File Size : 41,5 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Neutrosophic Duplets and Their Properties by Vasantha Kandasamy W.B. ,Ilanthenral Kandasamy ,Florentin Smarandache Pdf

The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache.

Author : Qiaoyan Li ,Yingcang Ma,Xiaohong Zhang,Juanjuan Zhang
Publisher : Infinite Study
Page : 13 pages
File Size : 48,8 Mb
Release : 2024-06-03
Category : Mathematics
ISBN : 8210379456XXX

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Study on the Algebraic Structure of Refined Neutrosophic Numbers by Qiaoyan Li ,Yingcang Ma,Xiaohong Zhang,Juanjuan Zhang Pdf

This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator and multiplication operator on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element and opposite elements of each refined neutrosophic number are given.