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Journal articles on the topic 'Neutrosophic number'

Author: Grafiati
Published: 2 June 2025
Last updated: 31 July 2025

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1

D. Sasikala. "On Determining Shortest Path Problem under Pentagonal Neutrosophic Fuzzy Number." Communications on Applied Nonlinear Analysis 31, no. 2s (2024): 09–16. http://dx.doi.org/10.52783/cana.v31.588.

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Neutrosophic sets is the generalization of fuzzy set theory. In this discipline the crucial situation are widely explained in three components appear in it in distinct fields. The study of Neutrosophy deals with the interactions of different ideational spectra. And also the shortest path method is one of the important tool in network analysis. In this approach the pentagonal neutrosophic fuzzy number is applied to determine the shortest path. A score function is used to defuzzify the number into crisp number. The new algorithm evaluates the shortest path for pentagonal neutrosophic fuzzy envir
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2

Ishtiaq, Umar, Khaleel Ahmad, Farhan Ali, Moazzama Faraz, and Ioannis K. Argyros. "Common Fixed-Point Theorems for Families of Compatible Mappings in Neutrosophic Metric Spaces." Foundations 3, no. 4 (2023): 738–65. http://dx.doi.org/10.3390/foundations3040042.

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Sets, probability, and neutrosophic logic are all topics covered by neutrosophy. Moreover, the classical set, fuzzy set, and intuitionistic fuzzy set are generalized using the neutrosophic set. A neutrosophic set is a mathematical concept used to solve problems with inconsistent, ambiguous, and inaccurate data. In this article, we demonstrate some basic fixed-point theorems for any even number of compatible mappings in complete neutrosophic metric spaces. Our primary findings expand and generalize the findings previously established in the literature.
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3

.., Hasan G�, Selçuk Topal, and Florentin Smarandache. "Neutrosophic Number Sequences: An introductory Study." International Journal of Neutrosophic Science 20, no. 1 (2023): 27–48. http://dx.doi.org/10.54216/ijns.200103.

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In this paper, Neutrosophic definitions and properties of some special number sequences which are frequently found in the science literature, called Neutrosophic Number Sequences (NNSq) via Horadam sequence are studied for the first time. Especially for Neutrosophic Fibonacci (NFNq) and Neutrosophic Lucas (NLNq) number sequences, fundamental properties and identities such as Ruggles, Honsberger, Cassini, Catalan, d’Ocagne, and Tagiuri are given. In addition, Neutrosophic definitions of the sequences of Pell (NPNq), Pell-Lucas (NPLNq), Jacobsthal (NJNq), Jacobsthal-Lucas (NJLNq), Mersenne (NMNq
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4

Smarandache, Florentin. "Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set." Mathematics 7, no. 4 (2019): 353. http://dx.doi.org/10.3390/math7040353.

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In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.
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.., N. Jose Parvin, S. Ghousia Begum, A. Rajkumar, D. Nagarajan, and Broumi Said. "Nonagonal Neutrosophic Number and its Application in Optimization Technique." International Journal of Neutrosophic Science 19, no. 2 (2022): 66–79. http://dx.doi.org/10.54216/ijns.190206.

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This article discusses Nonagonal Neutrosophic number and m-valued Nonagonal Neutrosophic number. The score function, the accuracy function, hamming distance, normalized hamming distance, Euclidean distance and normalized Euclidean distance of Nonagonal and m-polar Nonagonal Neutrosophic number are derived. Some de-neutrosophication method for Nonagonal Neutrosophic number and some properties of m-valued Nonagonal Neutrosophic number are proved. In this article the optimal path of an acyclic network is estimated using Neutrosophic α-cut grade, Neutrosophic Euclidean grade technique and dynamic
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6

Ye, Jun. "Neutrosophic number linear programming method and its application under neutrosophic number environments." Soft Computing 22, no. 14 (2017): 4639–46. http://dx.doi.org/10.1007/s00500-017-2646-z.

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Chakraborty, Avishek, Sankar Prasad Mondal, Ali Ahmadian, Norazak Senu, Shariful Alam, and Soheil Salahshour. "Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications." Symmetry 10, no. 8 (2018): 327. http://dx.doi.org/10.3390/sym10080327.

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In this paper, we introduce the concept of neutrosophic number from different viewpoints. We define different types of linear and non-linear generalized triangular neutrosophic numbers which are very important for uncertainty theory. We introduced the de-neutrosophication concept for neutrosophic number for triangular neutrosophic numbers. This concept helps us to convert a neutrosophic number into a crisp number. The concepts are followed by two application, namely in imprecise project evaluation review technique and route selection problem.
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8

Henry, Garrett. "Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph." Neutrosophic Sets and Systems 49 (April 26, 2022): 531–61. https://doi.org/10.5281/zenodo.6491498.

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New setting is introduced to study dominating, resolving, coloring, Eulerian(Hamiltonian) neu- trosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alli
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9

Fan, Feng, and Hu. "Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making." Mathematics 7, no. 5 (2019): 389. http://dx.doi.org/10.3390/math7050389.

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Linguistic neutrosophic numbers (LNNs) include single-value neutrosophic numbers and linguistic variable numbers, which have been proposed by Fang and Ye. In this paper, we define the linguistic neutrosophic number Einstein sum, linguistic neutrosophic number Einstein product, and linguistic neutrosophic number Einstein exponentiation operations based on the Einstein operation. Then, we analyze some of the relationships between these operations. For LNN aggregation problems, we put forward two kinds of LNN aggregation operators, one is the LNN Einstein weighted average operator and the other i
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10

Sabir majeed, Amir, and Nabeel Ezzulddin Arif. "Domination (set and Number) in Neutrosophic Soft over Graphs." Wasit Journal of Pure sciences 1, no. 3 (2022): 26–43. http://dx.doi.org/10.31185/wjps.65.

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By combining the ideas of neutrosophic soft sets and oversets in graphs and replacing each crisp or neutrosophic set by overset at each vertex and edge, we present a new framework for treating neutrosophic soft information (NSI) in this research.
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11

Ye, Jun. "Multiple-Attribute Group Decision-Making Method under a Neutrosophic Number Environment." Journal of Intelligent Systems 25, no. 3 (2016): 377–86. http://dx.doi.org/10.1515/jisys-2014-0149.

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AbstractAs a neutrosophic number, which consists of a determinate part and an indeterminate part, can more easily and better express incomplete and indeterminate information that exists commonly in real situations, the main purposes of this paper are to provide a neutrosophic number tool for group decision-making problems with indeterminate information under a neutrosophic number environment and to develop a de-neutrosophication method and a possibility degree ranking method for neutrosophic numbers from the probability viewpoint as a methodological support for group decision-making problems.
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12

.., A. Alrida, Katy D. Ahmad, and Rozina Ali. "On Some Open Problems About n-Cyclic Refined Neutrosophic Rings And Number Theory." Journal of Neutrosophic and Fuzzy Systems 3, no. 2 (2022): 37–42. http://dx.doi.org/10.54216/jnfs.030204.

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The objective of this paper is to present 40 open problems about the n-cyclic refined neutrosophic rings. These questions concern the n-cyclic refined neutrosophic rings, n-cyclic refined neutrosophic number theory, and n-cyclic refined neutrosophic analysis. They will represent the future of the study of neutrosophic n-cyclic refined rings and the related structures.
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13

ORHAN, ECEMIŞ, ŞAHIN MEMET, and KARGIN ABDULLAH. "SINGLE VALUED NEUTROSOPHIC NUMBER VALUED GENERALIZED NEUTROSOPHIC TRIPLET GROUPS AND ITS APPLICATIONS FOR DECISION MAKING APPLICATIONS." September 10, 2018. https://doi.org/10.5281/zenodo.1413893.

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Neutrosophy is a branch of philosophy. Neutrosophy is based on neutrosophic logic, neutrosophic probability and neutrosophic set. Neutrosophic triplet theory is new structure in neutrosophic set theory. In this study; we introduced notion of generalized neutrosophic triplet group. We defined contrary element for generalized neutrosophic triplet group.
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14

Debapriya, Mondal, Tudu Suklal, Chandra Roy Gopal, and Kumar Roy Tapan. "A Model Describing the Neutrosophic Differential Equation and Its Application On Mine Safety." September 7, 2021. https://doi.org/10.5281/zenodo.5486247.

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In the theory of uncertainty and approximation neutrosophy plays a significant role. Neutrosophy is tool emerged on standard or non-standard to measured the mathematical model of uncertainty, vagueness, ambiguity etc. In light of these major issues, the paper outlines of Neutrosophic Set, Single Valued Neutrosophic Set, Triangular Single Valued Neutrosophic Number and Trapezoidal Single Valued Neutrosophic Number. It also propose Neutrosophic Differential Equation and shown its solution in different conditions. Thereafter mining safety model via Single Valued neutrosophic number be epitomized.
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Debapriya, Mondal, Tudu Suklal, Chandra Roy Gopal, and Kumar Roy Tapan. "A Model Describing the Neutrosophic Differential Equation and Its Application on Mine Safety." October 7, 2021. https://doi.org/10.5281/zenodo.5553544.

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In the theory of uncertainty and approximation neutrosophy plays a significant role. Neutrosophy is tool emerged on standard or non-standard to measured the mathematical model of uncertainty, vagueness, ambiguity etc. In light of these major issues, the paper outlines of Neutrosophic Set, Single Valued Neutrosophic Set, Triangular Single Valued Neutrosophic Number and Trapezoidal Single Valued Neutrosophic Number. It also propose Neutrosophic Differential Equation and shown its solution in different conditions. Thereafter mining safety model via Single Valued neutrosophic number be epitomized.
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16

Henry, Garrett. "0034 | Chromatic Number and Neutrosophic Chromatic Number." December 9, 2021. https://doi.org/10.5281/zenodo.6319891.

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New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each c
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17

Henry, Garrett. "0034 | Chromatic Number and Neutrosophic Chromatic Number." December 10, 2021. https://doi.org/10.5281/zenodo.6319897.

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New setting is introduced to study chromatic number. Neutrosophic chromatic number and chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each c
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18

Henry, Garrett. "New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers." February 23, 2023. https://doi.org/10.13140/RG.2.2.33103.76968.

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“#168 Article” Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968). @ResearchGate: https://www.researchgate.net/publication/368752952   \documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode chara
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19

"Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs." Journal of Current Trends in Computer Science Research 2, no. 1 (2023). http://dx.doi.org/10.33140/jctcsr.02.01.04.

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New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, codegree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophi
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20

Florentin, Smarandache. "Refined Literal Indeterminacy and the Multiplication Law of Subindeterminacies." September 6, 2015. https://doi.org/10.5281/zenodo.49153.

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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 dual number, neutrosophic special dual number, neutrosophic special quasi dual number, neutrosophic linguistic number, neutrosophic linguistic interval-style number, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. 
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Henry, Garrett. "0053 | Clique Number in Neutrosophic Graphs." March 1, 2022. https://doi.org/10.5281/zenodo.6319650.

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New setting is introduced to study neutrosophic clique number and clique neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic clique number and clique neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then clique number C(NTG) for a neutrosophic gra
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Henry, Garrett. "0053 | Clique Number in Neutrosophic Graphs." March 1, 2022. https://doi.org/10.13140/RG.2.2.28338.68800.

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New setting is introduced to study neutrosophic clique number and clique neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic clique number and clique neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then clique number C(NTG) for a neutrosophic gra
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Henry, Garrett. "0058 | Matching Number in Neutrosophic Graphs." March 17, 2022. https://doi.org/10.13140/RG.2.2.18609.86882.

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New setting is introduced to study matching number and matching neutrosophic-number arising from edges. Being endpoints for two edges, simultaneously is key type of approach to have these notions namely neutrosophic matching number and matching neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have any edges which have no common edge inside set. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then matching number M(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximum cardinality of a set S of
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Henry, Garrett. "0026 | Neutrosophic Chromatic Number." March 1, 2022. https://doi.org/10.5281/zenodo.6320213.

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Different edges define new form of connections amid vertices. Thus defining new notion of coloring is possible when the connections of vertices which determine new color and it’s decider whether using new color or not, have been considered if they’ve special edges. The tools to define specific edges are studied. One notion is to use the connectedness to have two different types of numbers which are neutrosophic chromatic number and chromatic number. Other notion is to use the idea of neutrosophic strong to get specific edges which are eligible to define new numbers. Some classes of
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Henry, Garrett. "0051 | Failed Independent Number in Neutrosophic Graphs." February 25, 2022. https://doi.org/10.13140/RG.2.2.31196.05768.

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New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic graph.
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Henry, Garrett. "0054 | Failed Clique Number in Neutrosophic Graphs." March 3, 2022. https://doi.org/10.13140/RG.2.2.36039.16800.

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New setting is introduced to study neutrosophic failed-clique number and failed clique neutrosophic-number arising being out of neighborhood of vertices. Being out of neighbor is a key term to have these notions. Not having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-clique number and failed clique neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding smallest set which doesn’t have any vertex which is neighbor. Let NTG : (V,E,σ,μ) be a neutrosop
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27

Alhasan, Yaser Ahmad. "Concepts of Neutrosophic Complex Numbers." International Journal of Neutrosophic Science, 2020, 09–18. http://dx.doi.org/10.54216/ijns.080101.

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In this paper, concept of neutrosophic complex numbers and its properties were presented inculding the conjugate of neutrosophic complex number, division of neutrosophic complex numbers, the inverted neutrosophic complex number and the absolute value of a neutrosophic complex number. Theories related to the conjugate of neutrosophic complex numbers are proved, the product of a neutrosophic complex number by its conjugate equals the absolute value of number is also proved. This is an important introduction to define neutrosophic complex numbers in polar.
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Yaser, Ahmad Alhasan. "Concepts of Neutrosophic Complex Numbers." August 19, 2020. https://doi.org/10.5281/zenodo.3991433.

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In this paper, concept of neutrosophic complex numbers and its properties were presented inculding the conjugate of neutrosophic complex number, division of neutrosophic complex numbers, the inverted neutrosophic complex number and the absolute value of a neutrosophic complex number. Theories related to the conjugate of neutrosophic complex numbers are proved, the product of  a neutrosophic complex number by its conjugate equals the absolute value of number is also proved. This is an important introduction to define neutrosophic complex numbers in polar. 
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Memet, Şahin, and Kargın Abdullah. "Neutrosophic Triplet Group Based on Set Valued Neutrosophic Quadruple Numbers." December 10, 2019. https://doi.org/10.5281/zenodo.3569671.

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Smarandache introduced neutrosophic quadruple sets and neutrosophic quadruple numbers [45] in 2015. These sets and numbers are real or complex number valued. In this study, we firstly introduce set valued neutrosophic quadruple sets and numbers. We give some known and special operations for set valued neutrosophic quadruple numbers. Furthermore, Smarandache and Ali obtained neutrosophic triplet groups [30] in 2016. In this study, we firstly give neutrosophic triplet groups based on set valued neutrosophic quadruple number thanks to operations for set valued neutrosophic quadruple numbers. In t
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Henry, Garrett. "0047 | Zero Forcing Number in Neutrosophic Graphs." February 15, 2022. https://doi.org/10.13140/RG.2.2.32265.93286.

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New setting is introduced to study zero forcing number and zero forcing neutrosophic-number. Leaf-like is a key term to have these notions. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then zero forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is minimum cardinality of a set S of black vertices (whereas vertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of “the color-change rule”: a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Zero forcing neutro
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Henry, Garrett. "Regularity of Every Element to Function in the Type of Domination in Neutrosophic Graphs." September 3, 2022. https://doi.org/10.13140/RG.2.2.22861.10727.

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New setting is introduced to study k-number-dominating number and neutrosophic k-number-dominating number arising from k-number-dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. Minimum number of k-number-dominated vertices, is a number which is representative based on those vertices. Minimum neutrosophic number of k-number-dominated vertices corresponded to k-number-dominating set is called neutrosophic k-number-dominating number. Forming sets from k-number-dominated vertices to figure out different types of number of vertices in the sets from k-number-dominated sets
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Henry, Garrett. "0051 of 0054 | Failed Independent Number in Neutrosophic Graphs." March 4, 2022. https://doi.org/10.20944/preprints202202.0334.v2.

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  New setting is introduced to study neutrosophic failed-independent number and failed independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. Having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-independent number and failed independent neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding biggest set which have all vertices which are neighbors. Let NTG : (V,E,σ,μ) be a neutrosophic
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Henry, Garrett. "0052 | (Failed) 1-independent Number in Neutrosophic Graphs." February 27, 2022. https://doi.org/10.13140/RG.2.2.30593.12643.

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New setting is introduced to study 1-independent number, 1-independent neutrosophic-number, failed 1-independent number and failed 1-independent neutrosophic-number arising neighborhood of different vertices. Neighbor is a key term to have these notions. (Not) Having all possible edges amid vertices in a set is a key type of approach to have these notions namely 1-independent number, 1-independent neutrosophic-number, failed 1-independent number and failed 1-independent neutrosophic-number. Four numbers are obtained but now four settings leads to approach is on demand which is finding biggest
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Henry, Garrett. "Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs." November 20, 2022. https://doi.org/10.5281/zenodo.7363166.

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New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co- degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r; n)-regular hypergraphs and neutrosophic complete r-partite hypergraphs are proposed in this way, some results are obtained. General classes of
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Henry, Garrett. "0038 | Co-degree and Degree of classes of Neutrosophic Hypergraphs." January 4, 2022. https://doi.org/10.13140/RG.2.2.32672.10249.

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New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General classes o
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Henry, Garrett. "Recognition of the Pattern for Vertices to Make Dimension by Resolving in some Classes of Neutrosophic Graphs." September 14, 2022. https://doi.org/10.13140/RG.2.2.27281.51046.

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New setting is introduced to study k-number-resolving number and neutrosophic k-number-resolving number arising from k-number-resolved vertices in neutrosophic graphs assigned to neutrosophic graphs. Minimum number of k-number-resolved vertices, is a number which is representative based on those vertices. Minimum neutrosophic number of k-number-resolved vertices corresponded to k-number-resolving set is called neutrosophic k-number-resolving number. Forming sets from k-number-resolved vertices to figure out different types of number of vertices in the sets from k-number-resolved sets in the te
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37

M., Al-Tahan, and Davvaz B. "Refined neutrosophic quadruple (po-)hypergroups and their fundamental group." July 9, 2019. https://doi.org/10.5281/zenodo.3275550.

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After introducing the notion of hyperstructures about 80 years ago by F. Marty, a number of researches on its theory, generalization, and it’s applications have been done. On the other hand, the theory of Neutrosophy, the study of neutralities, was developed in 1995 by F. Smarandache as an extension of dialectics. This paper aims at finding a connection between refined neutrosophy of sets and hypergroups. In this regard, we define refined neutrosophic quadruple hypergroups, study their properties, and find their fundamental refined neutrosophic quadruple groups. Moreover, some results re
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Henry, Garrett. "0055 | (Failed) 1-clique Number in Neutrosophic Graphs." March 7, 2022. https://doi.org/10.13140/RG.2.2.14241.89449.

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New setting is introduced to study 1-clique number, 1-clique neutrosophic-number, failed 1-clique number and failed 1-clique neutrosophic-number arising being (out of) neighborhood of vertices. Being (out of) neighbor is a key term to have these notions. Not having all possible edges amid vertices in a set is a key type of approach to have these notions namely neutrosophic failed-1-clique number and failed 1-clique neutrosophic-number. Two numbers are obtained but now both settings leads to approach is on demand which is finding (biggest) smallest set which (doesn’t) have any vertex whic
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39

Henry, Garrett. "0038 | Co-degree and Degree of classes of Neutrosophic Hypergraphs." January 5, 2022. https://doi.org/10.5281/zenodo.6319940.

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  New setting is introduced to study types of coloring numbers, degree of vertices, degree of hyperedges, co-degree of vertices, co-degree of hyperedges, neutrosophic degree of vertices, neutrosophic degree of hyperedges, neutrosophic co-degree of vertices, neutrosophic co-degree of hyperedges, neutrosophic number of vertices, neutrosophic number of hyperedges in neutrosophic hypergraphs. Different types of procedures including neutrosophic (r, n)−regular hypergraphs and neutrosophic complete r−partite hypergraphs are proposed in this way, some results are obtained. General cl
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40

Henry, Garrett. "0048 | Failed Zero-Forcing Number in Neutrosophic Graphs." February 17, 2022. https://doi.org/10.13140/RG.2.2.24873.47209.

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New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a
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41

Henry, Garrett. "0048 | Failed Zero-Forcing Number in Neutrosophic Graphs." February 26, 2022. https://doi.org/10.20944/preprints202202.0343.v1.

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New setting is introduced to study failed zero-forcing number and failed zero-forcing neutrosophic-number. Leaf-like is a key term to have these notions. Forcing a vertex to change its color is a type of approach to force that vertex to be zero-like. Forcing a vertex which is only neighbor for zero-like vertex to be zero-like vertex but now reverse approach is on demand which is finding biggest set which doesn’t force. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then failed zero-forcing number Z(NTG) for a neutrosophic graph NTG : (V,E,σ,μ) is maximal cardinality of a
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42

Henry, Garrett. "0036 | Different Types of Neutrosophic Chromatic Number." December 20, 2021. https://doi.org/10.13140/RG.2.2.19068.46723.

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New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices whi
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43

Henry, Garrett. "0036 | Different Types of Neutrosophic Chromatic Number." December 21, 2021. https://doi.org/10.5281/zenodo.6319912.

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New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices whi
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44

Neutrosophic, Sets and Systems. "The neutrosophic quaternions numbers." February 17, 2024. https://doi.org/10.5281/zenodo.10674524.

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<strong>Abstract</strong>: This article aims to study the neutrosophic quaternion numbers, where we defined the neutrosophic quaternions numbers and the two equal neutrosophic quaternions numbers, also, the neutrosophic quaternions numbers algebra were introduced by studying addition, multiplication, division and conjugate of a neutrosophic quaternions number. In addition,<strong> </strong>we have discussed how to calculate the absolute value of a neutrosophic quaternions number and its inverted.
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A., A. A. Agboola, Davvaz B., and Smarandache F. "Neutrosophic quadruple algebraic hyperstructures." July 12, 2017. https://doi.org/10.5281/zenodo.888880.

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The objective of this paper is to develop neutrosophic quadruple algebraic hyperstructures. Specically, we develop neutrosophic quadruple semihypergroups, neutrosophic quadruple canonical hypergroups and neutrosophic quadruple hyperrings and we present elementary properties which characterize them.
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46

Said, Broumi, Bakali Assia, Talea Mohamed, Smarandache Florentin, Uluçay Vakkas, and Sahin Mehmet. "Neutrosophic Sets: An Overview." April 30, 2018. https://doi.org/10.5281/zenodo.1237940.

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In this study, we give some concepts concerning the neutrosophic sets, single valued neutrosophic sets, interval-valued neutrosophic sets, bipolar neutrosophic sets, neutrosophic hesitant fuzzy sets, inter-valued neutrosophic hesitant fuzzy sets, refined neutrosophic sets, bipolar neutrosophic refined sets, multi-valued neutrosophic sets, simplified neutrosophic linguistic sets, neutrosophic over/off/under sets, rough neutrosophic sets, rough bipolar neutrosophic sets, rough neutrosophic hyper-complex set, and their basic operations. Then we introduce triangular neutrosophic numbers, trapezoid
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47

Alhasan, Yaser Ahmad. "The General Exponential form of a Neutrosophic Complex Number." November 16, 2020. https://doi.org/10.5281/zenodo.4276371.

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In this paper, the general exponential form of a neutrosophic complex number is defined by virtue of the formula for indeterminacy in the angle is the indeterminate angle between two indeterminate parts of the coordinate axes and the general trigonometric form of a neutrosophic complex number is defined. In addition, we also provide theorems with proofs for how to find the conjugate of neutrosophic complex numbers by using the general exponential form, division of neutrosophic complex numbers by the general exponential form, multiplying two neutrosophic complex numbers by the general exponenti
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48

Erick, González-Caballero, Leyva-Vázquez Maikel, and Smarandache Florentin. "On neutrosophic uninorms." September 7, 2021. https://doi.org/10.5281/zenodo.5486462.

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Uninorm generalizes the notion of t-norm and t-conorm in fuzzy logic theory. They are three increasing, commutative and associate operators having one neutral element. However, such specific value identifies the kind of operator it is; t-norms have the 1 as neutral element, t-conorms have the 0 and uninorms have every number lying between 0 and 1. Uninorms have been applied as aggregators in many fields of Artificial Intelligence and Decision Making. This theory has also been extended to the framework of interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzz
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49

Henry, Garrett. "Dense Numbers and Minimal Dense Sets of Neutrosophic Graphs." May 4, 2022. https://doi.org/10.13140/RG.2.2.28044.59527.

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New setting is introduced to study dense number and neutrosophic dense number arising from neighborhood and the number of neighbors in neutrosophic graphs assigned to neutrosophic graphs. Consider a vertex. Maximum number of neighbors based on that vertex to compare to its neighbors, is a number which is representative based on that vertex. Minimum neutrosophic number of vertices amid neutrosophic cardinality of all sets of vertices is called neutrosophic dense number. Forming sets from special vertices to figure out different types of number of neighborhoods in the terms of largest number of
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50

Mohammad, Abobala, and Ibrahim Muritala. "An Introduction To Refined Neutrosophic Number Theory." September 7, 2021. https://doi.org/10.5281/zenodo.5485408.

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Number theory is concerned with properties of integers and Diophantine equations. The objective of this paper is dedicated to introduce the basic concepts in refined neutrosophic number theory such as division, divisors, congruencies, and Pell&#39;s equation in the refined neutrosophic ring of integers Z(𝐼1 ,𝐼2). Also, algorithms to solve refined neutrosophic linear congruencies and refined neutrosophic Pell&#39;s equation will be presented and discussed
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