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Relevant bibliographies by topics / Neutrosophic quadruple number

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Academic literature on the topic 'Neutrosophic quadruple number'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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Journal articles on the topic "Neutrosophic quadruple number"

1

Alifviansyah, Kevin, and Agung Lukito. "BCK-Aljabar Kuadrupel Neutrosofik." MATHunesa: Jurnal Ilmiah Matematika 10, no. 1 (2022): 226–38. http://dx.doi.org/10.26740/mathunesa.v10n1.p226-238.

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Artikel ini memperkenalkan bilangan kuadrupel neutrosofik yang berbasis pada suatu himpunan untuk mengonstruksi BCK-aljabar kuadrupel neutrosofik. Kemudian diselidiki beberapa sifatnya dan akan dipelajari konsep ideal, ideal implikatif positif, ideal tertutup pada BCK-aljabar kuadrupel neutrosofik. Untuk subhimpunan dan dari BCK/BCI-aljabar kuadrupel neutrosofik, akan dikaji himpunan yang terdiri atas bilangan kuadrupel neutrosofik dengan syarat tertentu. Akan disajikan beberapa syarat agar himpunan menjadi ideal implikatif positif pada BCK-Aljabar kuadrupel neutrosofik dan himpunan menjadi id

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2

Jun, Young Bae, Seok-Zun Song, and Seon Jeong Kim. "Neutrosophic Quadruple BCI-Positive Implicative Ideals." Mathematics 7, no. 5 (2019): 385. http://dx.doi.org/10.3390/math7050385.

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By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part ( a ) and an unknown part ( b T , c I , d F ) where T , I , F have their usual neutrosophic logic meanings and a , b , c , d are real or complex numbers, Smarandache introduced the concept of neutrosophic quadruple numbers. Using the concept of neutrosophic quadruple numbers based on a set, Jun et al. constructed neutrosophic quadruple BCK/BCI-algebras and implicative neutrosophic quadruple BCK-algebras. The notion of a neutrosophic quadruple BCI-positive implicative ideal is introduced, and

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3

Li, Qiaoyan, Yingcang Ma, Xiaohong Zhang, and Juanjuan Zhang. "Neutrosophic Extended Triplet Group Based on Neutrosophic Quadruple Numbers." Symmetry 11, no. 5 (2019): 696. http://dx.doi.org/10.3390/sym11050696.

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In this paper, we explore the algebra structure based on neutrosophic quadruple numbers. Moreover, two kinds of degradation algebra systems of neutrosophic quadruple numbers are introduced. In particular, the following results are strictly proved: (1) the set of neutrosophic quadruple numbers with a multiplication operation is a neutrosophic extended triplet group; (2) the neutral element of each neutrosophic quadruple number is unique and there are only sixteen different neutral elements in all of neutrosophic quadruple numbers; (3) the set which has same neutral element is closed with respec

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4

Şahin, Memet, and Arif Sarıoğlan. "Neutrosophic Quadruple Metric Spaces." Symmetry 17, no. 7 (2025): 1096. https://doi.org/10.3390/sym17071096.

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Instead of measuring the distance between two points with a positive real number, determining the degree to which the distance between these two points is close, not close, or uncertain allows for more detailed measurement. Recently, researchers have overcome this grading problem by using probability distribution functions, along with fuzzy, intuitionistic fuzzy, and neutrosophic sets. This study pioneers neutrosophic quadruple metric spaces as a powerful new tool for quantifying distances under complex, multi-dimensional uncertainty. It provides a comprehensive mathematical structure, includi

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5

Li, Qiaoyan, Yingcang Ma, Xiaohong Zhang, and Juanjuan Zhang. "Study on the Algebraic Structure of Refined Neutrosophic Numbers." Symmetry 11, no. 8 (2019): 954. http://dx.doi.org/10.3390/sym11080954.

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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

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6

Iampan, Aiyared, Metawee Songsaeng, and Ghulam Muhiuddin. "Fuzzy Duplex UP-Algebras." European Journal of Pure and Applied Mathematics 13, no. 3 (2020): 459–71. http://dx.doi.org/10.29020/nybg.ejpam.v13i3.3752.

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Using the concept of a neutrosophic quadruple number to a fuzzy duplex number, we introduce the notion of a fuzzy duplex UP-algebra, and investigate some related properties. Also, we find the necessary condition for a fuzzy duplex UP-set to be a fuzzy duplex UP-algebra. Furthermore, we study the relationship between special subsets of a UP-algebra and special subsets of a fuzzy duplex UP-set.

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7

Muhiuddin, G., Ahmad Al-Kenani, Eun Roh, and Young Jun. "Implicative Neutrosophic Quadruple BCK-Algebras and Ideals." Symmetry 11, no. 2 (2019): 277. http://dx.doi.org/10.3390/sym11020277.

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A neutrosophic set is initiated by Smarandache, and it is a novel tool to deal with vagueness considering the truth, indeterminacy and falsity memberships satisfying the condition that their sum is less than 3. The concept of neutrosophic quadruple numbers was introduced by Florentin Smarandache. Using this idea, Jun et al. introduced the notion of neutrosophic quadruple B C K / B C I -numbers, and studied neutrosophic quadruple B C K / B C I -algebras. As a continuation of Jun et al.’s paper, the notion of implicative neutrosophic quadruple B C K -algebras is introduced, and several propertie

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8

W.B., Vasantha Kandasamy, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Quadruple Vector Spaces and Their Properties." Mathematics 7, no. 8 (2019): 758. http://dx.doi.org/10.3390/math7080758.

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In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals R or the field of complex numbers C or the finite field of characteristic p, Z p ; p a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector s

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9

Merkepci, Hamiyet, and Ahmed Hatip. "Algorithms for Computing Pythagoras Triples and 4-Tiples in Some Neutrosophic Commutative Rings." International Journal of Neutrosophic Science 20, no. 3 (2023): 107–14. http://dx.doi.org/10.54216/ijns.200310.

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This paper is dedicated to study the number theoretical Pythagoras triples\4-tiples problem in several kinds of neutrosophic algebraic systems, where it finds an algorithm to find Pythagoras triples\4-tiples in commutative neutrosophic rings and refined neutrosophic rings too. Besides, the necessary and sufficient condition for a triple\4-tiple to be Pythagoras triple\4-tiple (quadruples) is obtained and proven in term of theorems. In addition, many numerical examples will be illustrated.

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10

V., Christianto1* F. Smarandache2 M. Aslam3. "How we can extend the standard deviation notion with neutrosophic interval and quadruple neutrosophic numbers." International Journal of Neutrosophic Science (IJNS) 2, no. 2 (2020): 72–76. https://doi.org/10.5281/zenodo.3728218.

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