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Study on the Algebraic Structure of Refined Neutrosophic Numbers

Author: Qiaoyan Li

Publisher: Infinite Study

Published:

Total Pages: 13

ISBN-13:

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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.

Book Synopsis Study on the Algebraic Structure of Refined Neutrosophic Numbers by : Qiaoyan Li

Download or read book Study on the Algebraic Structure of Refined Neutrosophic Numbers written by Qiaoyan Li and published by Infinite Study. This book was released on with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

n-Refined Neutrosophic Groups I

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.

Book Synopsis n-Refined Neutrosophic Groups I by : Mohammad Abobala

Download or read book n-Refined Neutrosophic Groups I written by Mohammad Abobala and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to define for the first time the concept of n-refined neutrosophic group. This work is devoted to study some elementary properties of n-refined neutrosophic groups and to establish the algebraic basis of this structure such as n-refined neutrosophic subgroups, n-refined neutrosophic homomorphisms, and n-refined neutrosophic isomorphisms.

Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 6

ISBN-13:

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In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures.

Book Synopsis Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies by : Florentin Smarandache

Download or read book Refined Literal Indeterminacy and the Multiplication Law of Sub-Indeterminacies written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures.

On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings

Author: Mohammad Abobala

Publisher: Infinite Study

Published:

Total Pages: 8

ISBN-13:

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Idempotent elements in a ring 𝑅 are the elements with the condition 𝒂𝟐=𝒂. This paper introduces the criterion of any element in a refined neutrosophic ring to be idempotent. Also, the concept of symmetric and supersymmetric elements in a neutrosophic ring 𝑅(𝐼), and a refined neutrosophic ring 𝑅(𝐼1,𝐼2) are defined. Also, the invertibility of these elements is discussed.

Book Synopsis On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings by : Mohammad Abobala

Download or read book On Some Special Elements in Neutrosophic Rings and Refined Neutrosophic Rings written by Mohammad Abobala and published by Infinite Study. This book was released on with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Idempotent elements in a ring 𝑅 are the elements with the condition 𝒂𝟐=𝒂. This paper introduces the criterion of any element in a refined neutrosophic ring to be idempotent. Also, the concept of symmetric and supersymmetric elements in a neutrosophic ring 𝑅(𝐼), and a refined neutrosophic ring 𝑅(𝐼1,𝐼2) are defined. Also, the invertibility of these elements is discussed.

(t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited)

Author: Florentin Smarandache

Publisher: Infinite Study

Published:

Total Pages: 7

ISBN-13:

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This paper is an improvement of our paper “(t, i, f)-Neutrosophic Structures” [1], where we introduced for the first time a new type of structures, called (t, i, f)Neutrosophic Structures, presented from a neutrosophic logic perspective, and we showed particular cases of such structures in geometry and in algebra.

Book Synopsis (t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited) by : Florentin Smarandache

Download or read book (t, i, f)-Neutrosophic Structures & I-Neutrosophic Structures (Revisited) written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is an improvement of our paper “(t, i, f)-Neutrosophic Structures” [1], where we introduced for the first time a new type of structures, called (t, i, f)Neutrosophic Structures, presented from a neutrosophic logic perspective, and we showed particular cases of such structures in geometry and in algebra.

Author:

Publisher:

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Total Pages:

ISBN-13: 1599733811

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Download or read book written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

International Journal of Neutrosophic Science (IJNS) Volume 9, 2020

Author: Broumi Said

Publisher: Infinite Study

Published:

Total Pages: 116

ISBN-13:

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International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. Papers concern with neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributions to economics, finance, management, industries, electronics, and communications are promoted.

Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 9, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 9, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. Papers concern with neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributions to economics, finance, management, industries, electronics, and communications are promoted.

International Journal of Neutrosophic Science (IJNS) Volume 8, 2020

Author: Broumi Said

Publisher: Infinite Study

Published:

Total Pages: 126

ISBN-13:

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International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

Book Synopsis International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 by : Broumi Said

Download or read book International Journal of Neutrosophic Science (IJNS) Volume 8, 2020 written by Broumi Said and published by Infinite Study. This book was released on with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Journal of Neutrosophic Science (IJNS) is a peer-review journal publishing high quality experimental and theoretical research in all areas of Neutrosophic and its Applications. IJNS is published quarterly. IJNS is devoted to the publication of peer-reviewed original research papers lying in the domain of neutrosophic sets and systems. Papers submitted for possible publication may concern with foundations, neutrosophic logic and mathematical structures in the neutrosophic setting. Besides providing emphasis on topics like artificial intelligence, pattern recognition, image processing, robotics, decision making, data analysis, data mining, applications of neutrosophic mathematical theories contributing to economics, finance, management, industries, electronics, and communications are promoted.

Neutrosophic Sets and Systems, Vol. VIII

Author: Florentin Smarandache, Mumtaz Ali

Publisher: Infinite Study

Published: 2015-04-01

Total Pages: 70

ISBN-13: 1599733382

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This volume is a collection of ten papers by contributors F. Smarandache, F. Yuhua, K. Mondal, S. Pramanik, S. Broumi, J. Ye, A. A. Salama,, N. Easa, S. A. Elhafez, M. M. Lotfy, L. Kong, Y. Wu, P. Biswas, B. C. Giri, A. Mukkerjee, and S. Sarkar, focusing on a new kind of algebraic structures called (T, I, F)- Neutrosophic Structures; Expanding Uncertainty Principle to Certainty-Uncertainty Principles with Neutrosophy and Quad-stage Methods; Rough Neutrosophic Multi-Attribute Decision-Making Based on Rough Accuracy Score Function; an Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variable; Review of Recommender Systems Algorithms Utilized in Social Networks based e-Learning Systems & Neutrosophic System; Fault Diagnosis Method of Gasoline Engines Using the Cosine Similarity Measure of Neutrosophic Numbers; Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers; Thesis-Antithesis-Neutrothesis, and Neutrosynthesis; Negating Four Color Theorem with Neutrosophy and Quadstage Method; and A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems.

Book Synopsis Neutrosophic Sets and Systems, Vol. VIII by : Florentin Smarandache, Mumtaz Ali

Download or read book Neutrosophic Sets and Systems, Vol. VIII written by Florentin Smarandache, Mumtaz Ali and published by Infinite Study. This book was released on 2015-04-01 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of ten papers by contributors F. Smarandache, F. Yuhua, K. Mondal, S. Pramanik, S. Broumi, J. Ye, A. A. Salama,, N. Easa, S. A. Elhafez, M. M. Lotfy, L. Kong, Y. Wu, P. Biswas, B. C. Giri, A. Mukkerjee, and S. Sarkar, focusing on a new kind of algebraic structures called (T, I, F)- Neutrosophic Structures; Expanding Uncertainty Principle to Certainty-Uncertainty Principles with Neutrosophy and Quad-stage Methods; Rough Neutrosophic Multi-Attribute Decision-Making Based on Rough Accuracy Score Function; an Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variable; Review of Recommender Systems Algorithms Utilized in Social Networks based e-Learning Systems & Neutrosophic System; Fault Diagnosis Method of Gasoline Engines Using the Cosine Similarity Measure of Neutrosophic Numbers; Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers; Thesis-Antithesis-Neutrothesis, and Neutrosynthesis; Negating Four Color Theorem with Neutrosophy and Quadstage Method; and A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems.

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

Author: Florentin Smarandache

Publisher: MDPI

Published: 2019-11-27

Total Pages: 714

ISBN-13: 3039219383

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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.

Book Synopsis 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 by : Florentin Smarandache

Download or read book 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 written by Florentin Smarandache and published by MDPI. This book was released on 2019-11-27 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.