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Journal articles on the topic 'Neutrosophic set'

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

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1

Al-Odhari, Adel. "Some Aspects of Neutrosophic Set Theory." Neutrosophic Optimization and Intelligent Systems 4 (October 1, 2024): 31–38. http://dx.doi.org/10.61356/j.nois.2024.4359.

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This article aims to introduce my work on constructing neutrosophic set theory. Neutrosophy is a new branch of mathematical systems proposed by Smarandache in 1995 as an extension of an intuitionistic fuzzy set according to three-degree membership functions. The new perspective of neutrosophic sets consists of two paths, the first path depends on the three degrees including the degree of truth-membership, degree of indeterminacy-membership, and degree of false-non-membership respectively, while the second path depends on the generated classical set by three types of neutrosophic sets and study
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2

Mehmood, Arif, Saleem Abdullah, Mohammed M. Al-Shomrani, Muhammad Imran Khan, and Orawit Thinnukool. "Some Results in Neutrosophic Soft Topology Concerning Neutrosophic Soft ∗ b Open Sets." Journal of Function Spaces 2021 (May 24, 2021): 1–15. http://dx.doi.org/10.1155/2021/5544319.

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In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗ b open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗ b open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets. Then, with the application of this new definition, some soft neutrosophical separation axioms, countability theorems, and countable space can be Hausdorff space under the subjection of neutrosophic soft sequence which is convergent, the cardinality of neutrosophic soft countable space, engagement of neutrosophic soft counta
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3

Et. al., N. Moogambigai. "Z-open sets in a Neutrosophic Topological Spaces." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1S (2021): 357–62. http://dx.doi.org/10.17762/turcomat.v12i1s.1850.

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In this paper, introduce a neutrosophicopen sets in neutrosophic topological spaces. Also, discuss about near open sets, their properties and examplesZ-open set which is a union of neutrosophic P-open sets and neutrosophic δof a neutrosophicS Z-open set. Moreover, we investigate some of their basic properties and examples of neutrosophic Z-interior and Z-closure in a neutrosophic topological spaces.
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4

Al-Quran, Ashraf Al, Faisal Al Al-Sharqi, Hamiden Abd El Wahed Khalifa, Haifa Alqahtani, and Ali M. A. Bany Awad. "T-Spherical Fuzzy-Valued Neutrosophic Set Theory." International Journal of Neutrosophic Science 23, no. 2 (2024): 104–15. http://dx.doi.org/10.54216/ijns.230209.

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From fuzzy to neutrosophy, multiple hybrid models have been innovated, with each introduced model surpassing its predecessor. Due to the inherent indeterminacy in the world, a more precise form of imprecision is required. As a result, more sophisticated variants of the neutrosophic set have been created. Examples of these amalgamations include fuzzy neutrosophic sets, intuitionistic fuzzy neutrosophic sets, Pythagorean fuzzy neutrosophic sets, neutrosophic vague sets, and neutrosophic rough sets. The main objective of this paper is to present another variant of the neutrosophic set called T-sp
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5

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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6

Gulistan, Muhammad, Florentin Smarandache, and Amir Abdullah. "An application of complex neutrosophic sets to the theory of groups." International Journal of Algebra and Statistics 7, no. 1-2 (2018): 94–112. http://dx.doi.org/10.20454/ijas.2018.1455.

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In this article we introduce the concept of complex neutrosophıc subgroups (normal subgroups). We define the notion of alpha-cut of complex neutrosophıc set, give examples and study some of its related results. We also define the Cartesian product of complex neutrosophic subgroups. Furthermore, we introduce the concept of image and preimage of complex neutrosophic set and prove some of its properties.
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7

A.A., Salama, K.F.Alhasan, A. Elagamy H., and Smarandache Florentin. "Neutrosophic Dynamic Set." Neutrosophic Knowledge 3, no. 1 (2021): 1–5. https://doi.org/10.5281/zenodo.5507522.

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In this paper, we introduced the concept of the dynamic set according to modern logic, is neutrosophic logic. We study the neutrosophic dynamic set according to time and random variable depended on dynamic set. Neutrosophic dynamic is a dynamic analysis of a sequence of data through of time. It used in many problems in life such as a mathematical statistic, philosophy, medicine, engineering. Some examples and notes are presented.
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8

Ishtiaq, Umar, Khalil Javed, Fahim Uddin, Manuel de la Sen, Khalil Ahmed, and Muhammad Usman Ali. "Fixed Point Results in Orthogonal Neutrosophic Metric Spaces." Complexity 2021 (August 9, 2021): 1–18. http://dx.doi.org/10.1155/2021/2809657.

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Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metr
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9

Al-Odhari, Adel Mohammed. "Axiomatic of Neutrosophic Groups." مجلة جامعة صنعاء للعلوم التطبيقية والتكنولوجيا 2, no. 2 (2024): 205–14. http://dx.doi.org/10.59628/jast.v2i2.793.

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The aim of this article is to; present a neutrosophic group according to axioms such as classical group theory and the neutrosophic set, and to study some properties and theorems related to the neutrosophic group. The new concept of the neutrosophic set is a new approach that is suitable for mathematical problems related to philosophical concepts, such as uncertainty and indeterminacy, in which human knowledge and human evaluation are necessary. Neutrosophic algebra is a branch of neutrosophic set theory, and in 2004, Kandasamy and Smarandache introduced basic neutrosophic algebraic structures
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10

Surapati, Pramanik* Kalyan Mondal. "ROUGH BIPOLAR NEUTROSOPHIC SET." Global Journal of Engineering Science and Research Management 3, no. 6 (2016): 71–81. https://doi.org/10.5281/zenodo.55966.

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Bipolar neutrosophic set theory and rough neutrosophic set theory are emerging as powerful tool for dealing with uncertainty, and indeterminate, incomlete, and inprecise information. In the present study we develop a hybrid structure called “rough bipoar neutrsophic set”. In the study, we define rough bipoar neutrsophic set and define union, complement, intersection and containment of rough bipolar neutrosophic sets.  
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11

Haibin, Wang, Madiraju Praveen, Zhang Yanqing, and Sunderraman Rajshekhar. "Interval Neutrosophic Sets." September 7, 2014. https://doi.org/10.5281/zenodo.32260.

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Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the set-theoretic operators on an instance of neutrosophic set, we call it interval neutrosophic set (INS).We prove various properties of INS, which are connected to the operations and relations over INS. Fi
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12

Salama, A. A., and Elghawalby Hewayda. "Neutrosophic Crisp Set & Neutrosophic Crisp relations." July 1, 2015. https://doi.org/10.5281/zenodo.22579.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The purpose of this paper is to introduce a new type of neutrosophic crisp set as the *- neutrosophic crisp sets as a generalization to star intuitionistic set due to Indira et al.[4 ], and study some of its properties. Finally we introduce and study the notion of *- neutrosophic relation and some of its properties. .
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13

Haibin, Wang Yan-Qing Zhang Member IEEE Rajshekhar Sunderraman. "Truth-Value Based Interval Neutrosophic Sets." December 6, 2014. https://doi.org/10.5281/zenodo.34917.

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Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the set-theoretic operators on an instance of neutrosophic set, we call it truth-value based interval neutrosophic set. We provide various properties of truth-value based interval neutrosophic sets, which are connected to the operations
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14

Faruk, Karaaslan. "Correlation coefficients of single valued neutrosophic refined soft sets and their applications in clustering analysis." December 5, 2014. https://doi.org/10.5281/zenodo.34794.

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Neutrosophic set theory was introduced by Smarandache based on neutrosophy which is a branch of philosophy. The concept of single valued neutrosophic refined set was defined by Ye as an extension of single valued neutrosophic sets introduced by Wang. In this study, the concept of single valued neutrosophic refined soft set is defined as an extension of single valued neutrosophic refined set.
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15

Muhammad, Gulistan, Smarandache Florentin, and Abdullah Amir. "An application of complex neutrosophic sets to the theory of groups." May 18, 2019. https://doi.org/10.5281/zenodo.2837860.

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In this article we introduce the concept of complex neutrosophıc subgroups (normal subgroups). We define the notion of alpha-cut of complex neutrosophıc set, give examples and study some of its related results. We also define the Cartesian product of complex neutrosophic subgroups. Furthermore, we introduce the concept of image and preimage of complex neutrosophic set and prove some of its properties.
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16

Shawkat, Alkhazaleh. "Neutrosophic Vague Set Theory." July 1, 2015. https://doi.org/10.5281/zenodo.22602.

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In 1993, Gau and Buehrer proposed the theory of vague sets as an extension of fuzzy set theory. Vague sets are regarded as a special case of context-dependent fuzzy sets. In 1995, Smarandache talked for the first time about neutrosophy, and he defined the neutrosophic set theory as a new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. In this paper, we define the concept of a neutrosophic vague set as a combination of neutrosophic set and vague set. We also define and study the operations and properties of neutrosophic
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17

A.A.Salama and S.A.Alblowi. "Neutrosophic Set and Neutrosophic Topological Spaces." October 16, 2012. https://doi.org/10.5281/zenodo.23122.

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Neutrosophy has been introduced by Smarandache as a new branch of philosophy. The purpose of this paper is to construct a new set theory called the neutrosophic set. After given the fundamental definitions of neutrosophic set operations, we obtain several properties, and discussed the relationship between neutrosophic sets and others. Finally, we extend the concepts of fuzzy topological space and intuitionistic fuzzy topological spaceto the case of neutrosophic sets.
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18

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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19

Arulpandy, P., and Pricilla M. Trinita. "Bipolar neutrosophic soft generalized pre-closed sets and pre-open sets in topological space." April 9, 2022. https://doi.org/10.5281/zenodo.6426461.

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Neutrosophy is one of the widely used tool to deal with uncertainty. In recent years, neutrosophic sets were applied in the field of topology. There are numerous types of neutrosophic topological spaces based on different kinds of neutrosophic sets are proposed by research community. Bipolar neutrosophic set and their topological spaces were proposed and analyzed by many researchers. In this paper, the generalization of bipolar neutrosophic soft set and their classifications are proposed. A bipolar neutrosophic soft generalized pre-closed sets and bipolar neutrosophic soft generalized pre-open
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20

Broumi, Said, and Smarandache Florentin. "Intuitionistic Neutrosophic Soft Set." August 9, 2014. https://doi.org/10.5281/zenodo.30199.

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In this paper we study the concept of intuitionistic neutrosophic set of Bhowmik and Pal. We have introduced this concept in soft sets and def ned intuitionistic neutrosophic soft set. Some def nitions and operations have been introduced on intuitionistic neutrosophic soft set. Some properties of this concept have been established.
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21

SUDHAKAR.V.J, ALI. A. MOHAMED, and VINOTH.D. "INTERVAL VALUED SIGNED NEUTROSOPHIC GRAPH." May 20, 2019. https://doi.org/10.5281/zenodo.3053289.

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The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophicsets. We apply for the first time the concept of interval valued neutrosophic sets, an instance of neutrosophic sets, to the graph theory. We introduce certain types of interval valued signed neutrosophc graphs (IVNG) and investigate some of their properties with proof and example.
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22

Smarandache, Florentin. "Neutrosophic Probability, Set, And Logic (first version)." July 12, 2000. https://doi.org/10.5281/zenodo.57726.

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This project is a part of a National Science Foundation interdisciplinary project proposal. Starting from a new viewpoint in philosophy, the neutrosophy, one extends the classical "probability theory", "fuzzy set" and "fuzzy logic" to <neutrosophic probability>, <neutrosophic set> and <neutrosophic logic> respectively. They are useful in artificial intelligence, neural networks, evolutionary programming, neutrosophic dynamic systems, and quantum mechanics.
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23

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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25

SAID, BROUMI. "GeneralizedNeutrosophicSoftSet." April 10, 2013. https://doi.org/10.5281/zenodo.235719.

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In this paper we present a new concept called “generalized neutrosophic soft set”. This concept incorporates the beneficial properties of both generalized neutrosophic set introduced by A.A.Salama [7] and soft set techniques proposed by Molodtsov [4]. We also study some properties of this concept. Some definitions and operations have been introduced on generalized neutrosophic soft set. Finally we present an application of generalized neuutrosophic soft set in decision making problem.
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26

A., A. Salama. "Basic Structure of Some Classes of Neutrosophic Crisp Nearly Open Sets & Possible Application to GIS Topology." July 1, 2015. https://doi.org/10.5281/zenodo.22438.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. The fundamental concepts of neutrosophic set, introduced by Smarandache and Salama. In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. In this paper the structure of some classes of neutrosophic crisp nearly open sets are investigated and some applications are given. Finally we generalize the crisp topological and intuitioistic studies to the notion of neutrosop
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27

Hashem, Bordba, Long Xin Xiao, Ali Borzooei Rajab, and Bae Jun Young. "Positive implicative ideals of BCK-algebras based on neutrosophic sets and falling shadows." February 11, 2022. https://doi.org/10.5281/zenodo.6041290.

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Neutrosophy is introduced by F. Smarandache in 1980 which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy considers a proposition, theory, event, concept, or entity, ”A” in relation to its opposite, ”Anti-A” and that which is not A, ”Non-A”, and that which is neither ”A” nor ”Anti-A”, denoted by ”Neut-A”. Neutrosophy is the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, and neutrosophic statistics. In this article,
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28

Suman, Das, Das Rakhal, and Pramanik Surapati. "Topology on Ultra Neutrosophic Set." December 12, 2021. https://doi.org/10.5281/zenodo.5775098.

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In this paper, we introduce the ultra neutrosophic set, and define some operations and establish a few properties of the ultra neutrosophic sets. Using the notion of topology on ultra neutrosophic sets, we introduce the concept of ultra neutrosophic topology. Further, we define the notion of ultra neutrosophic interior and ultra neutrosophic closure via ultra neutrosophic topological space
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Eman.M.El-Nakeeb, ElGhawalby Hewayda, A.A.Salama, and S.A.El-Hafeez. "Neutrosophic Crisp Mathematical Morphology." June 19, 2017. https://doi.org/10.5281/zenodo.831937.

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In this paper, we aim to apply the concepts of the neutrosophic crisp sets and its operations to the classical mathematical morphological operations, introducing what we call "Neutrosophic Crisp Mathematical Morphology". Several operators are to be developed, including the neutrosophic crisp dilation, the neutrosophic crisp erosion, the neutrosophic crisp opening and the neutrosophic crisp closing.
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30

Surapati, Pramanik. "Interval Pentapartitioned Neutrosophic Sets." April 16, 2023. https://doi.org/10.5281/zenodo.7832745.

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Pentapartitioned neutrosophic set is a powerful mathematical tool, which is the extension of neutrosophic set and n-valued neutrosophic refined logic for better designing and modeling real-life problems. A generalization of the notion of pentapartitioned neutrosophic set is introduced. The new notion is called Interval Pentapartitioned Neutrosophic set (IPNS). Pentapartitioned neutrosophic set is developed by combining the pentapartitioned neutrosophic set and interval neutrosophic set. We define several set theoretic operations of IPNSs, namely, inclusion, complement, intersection. We also es
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31

Surapati, Pramanik. "Interval quadripartitioned Neutrosophic Sets." October 2, 2022. https://doi.org/10.5281/zenodo.7135267.

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Quadripartitioned neutrosophic set is a mathematical tool, which is the extension of neutrosophic set and n-valued neutrosophic refined logic for dealing with real-life problems. A generalization of the notion of quadripartitioned neutrosophic set is introduced. The new notion is called Interval Quadripartitioned Neutrosophic set (IQNS). Quadripartitioned neutrosophic set is developed by combining the Quadripartitioned neutrosophic set and interval neutrosophic set. Several set theoretic operations of IQNSs, namely, inclusion, complement, and intersection are defined. Various properties of set
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32

Vakeel, A. Khan, and Kamran Mohd. "Topological Aspects of Set-Valued Mappings Defned on Neutrosophic Normed Spaces." September 10, 2024. https://doi.org/10.5281/zenodo.13989232.

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 Samarandache [43] introduced neutrosophoic sets to generalize the theory of fuzzy sets. In this paper we modify the definition of neutrosophic normed space with help of continuous neutrosophic t-representable norm. Then we study the statistical graphical convergence and pointwise convergence of the sequences of setvalued functions defined on modified version of neutrosophic normed space and give some related theorems. We also introduce neutrosophic upper and lower semi continuities of set valued maps to develop the link between these convergences.
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33

Abdullah, Kargın, Dayan Azize, and Merve Şahin Necmiye. "Generalized Hamming Similarity Measure Based on Neutrosophic Quadruple Numbers and Its Applications to Law Sciences." February 18, 2021. https://doi.org/10.5281/zenodo.4549328.

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Neutrosophic quadruple numbers are the newest field studied in neutrosophy. Neutrosophic quadruple numbers, using the certain extent known data of an object or an idea, help us uncover their known part and moreover they allow us to evaluate the unknown part by the trueness, indeterminacy and falsity values. In this study, we generalized Hamming similarity measures for the generalized set-valued neutrosophic quadruple sets and numbers. We showed that generalized Hamming measure satisfies the similarity measure condition. Also, we generalized an algorithm for the generalized set-valued neutrosop
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34

Takallo, M. Mohseni, R.A. Borzooei, and Young Bae Jun. "MBJ-neutrosophic structures and its applications in BCK/BCI-algebras." Neutrosophic Sets and Systems 23 (December 10, 2018). https://doi.org/10.5281/zenodo.2155212.

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Smarandache (F. Smarandache. Neutrosophy, neutrosophic probability, set, and logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998) initiated neutrosophic sets which can be used as a mathematical tool for dealing with indeterminates and inconsistent information. As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced, and it is applied to BCK=BCI-algebras. The concept of MBJ-neutrosophic subalgebras in BCK=BCI-algebras is introduced, and related properties are investigated. A characterization of MBJ-neutrosophic subalgebra is pr
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35

J., Mohan, Guo Yanhui, Krishnaveni V., and Jeganathan Kanchana. "MRI Denoising Based on Neutrosophic Wiener Filtering." February 26, 2012. https://doi.org/10.5281/zenodo.34852.

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In this paper, a new filtering method is presents to remove Rician noise from magnetic resonance image. This filter is based on Neutrosophic set (NS) approach of wiener filtering. A Neutrosophic Set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra.
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36

R, Binu. "Neutrosophic Quotient Algebra." International Journal of Neutrosophic Science, 2019, 83–89. http://dx.doi.org/10.54216/ijns.000204.

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The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set. This paper expands the definition of quotient algebra within the context of neutrosophical set.
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37

Binu, R. "Neutrosophic Quotient Algebra." International Journal of Neutrosophic Science 0 / 2019 (December 1, 2019). https://doi.org/10.5281/zenodo.4018986.

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The algebraic properties of neutrosphic ideals over algebra, isomorphism properties of neutrosophic ideal and neutrosophic modules over algebra are discussed in this paper. Some of the charactrisations of Neutrosophic quotient algebra are derived and the role of algebraic structures is studied in the context of neutrosophic set. This paper expands the definition of quotient algebra within the context of neutrosophical set.
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38

Florentin, Smarandache. "Neutrosophic Measure and Neutrosophic Integral." January 15, 2013. https://doi.org/10.5281/zenodo.30224.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. We now introduce for the first time the notions of neutrosophic measure and neutrosophic integral. Neutrosophic Science means development and applications of neutrosophic logic/set/measure/integral/ probability etc. and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, dependin
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39

Said, Broumi, and Smarandache Florentin. "Interval Neutrosophic Rough Set." July 2, 2014. https://doi.org/10.5281/zenodo.30193.

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This paper combines interval-valued neutrosophic sets and rough sets. It studies rougheness in interval-valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower an upper approximations of interval neutrosophic sets.
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40

Tuhin, Bera, and Nirmal Kumar Mahapatra. "On Neutrosophic Normal Soft Groups." December 9, 2016. https://doi.org/10.5281/zenodo.235809.

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The concepts of neutrosophic normal soft group, neutrosophic soft cosets,neutrosophics of homomorphism are introduced and illustrated by suitable examples in this paper. Several related properties and structural characteristics are investigated. Some of their basic theorems are also established.
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41

Florentin, Smarandache. "Three Decades of Neutrosophic and Plithogenic Theories with their Applications (1995 - 2024)." September 10, 2024. https://doi.org/10.5281/zenodo.13989101.

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Zadeh introduced the degree of membership/truth (T) in 1965 and defined the fuzzy set. Atanassov introduced the degree of nonmembership/falsehood (F) in 1986 and defined the intuitionistic fuzzy set. Smarandache introduced the degree of indeterminacy/neutrality (I) as independent component in 1995 (published in 1998) and he defined the neutrosophic set on three components: (T, I, F) = (Truth, Indeterminacy, Falsehood), where in general T, I, F are subsets of the interval [0, 1]; in particular T, I, F may be intervals, hesitant sets, single-values, etc.; Indet
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42

Mumtaz, Ali, and Smarandache Florentin. "Complex neutrosophic set." December 21, 2015. https://doi.org/10.5281/zenodo.49143.

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p>Complex fuzzy sets and complex intuitionistic fuzzy sets cannot handle imprecise, indeterminate, inconsistent, and incomplete information of periodic nature. To overcome this difficulty, we introduce complex neutrosophic set. A complex neutrosophic set is a neutrosophic set whose complex-valued truth membership function, complex-valued indeterminacy membership function, and complex-valued falsehood membership functions are the combination of real-valued truth amplitude term in association with phase term, real-valued indeterminate amplitude term with phase term, and real-valued false ampli
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43

Surapati, Pramanik, Dalapati Shyamal, Alam Shariful, Kumar Roy Tapan, and Smarandache F. "Neutrosophic Cubic MCGDM Method Based on Similarity Measure." June 19, 2017. https://doi.org/10.5281/zenodo.831935.

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The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties. We present a new multi criteria group decision making method with linguistic variables in neutrosophic cubic set environment. Finally, we present a numerical example to demonstrate the usefulness and applicability of the proposed method.
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44

Bimal, Shil, Das Rakhal, and Das Suman. "Single Valued Pentaparitioned Neutrosophic Off-Set / Over-Set / Under-Set." October 2, 2022. https://doi.org/10.5281/zenodo.7135329.

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The main focus of this paper is to introduce the notion of single valued pentapartitioned neutrosophic off set / over set / under set. Besides, we establish several operations on single valued pentapartitioned neutrosophic off sets / over sets / under sets. Besides, we furnish some suitable examples to validate the results established in this article. Further, we establish some interesting results on single valued pentapartitioned neutrosophic off set / over set / under set. 
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Eser, Sert. "A new modified neutrosophic set segmentation approach." May 20, 2019. https://doi.org/10.5281/zenodo.3047147.

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Segmentation is paramount to 3D video systems employing multi-view video-plus-depth data (MVD) to implement free-viewpoint navigation and comfortable 3D viewing, mod- eling, and comprehension. The Neutrosophic Set (NS) concept relies on the neutrosophy theory dealing with structures, and it focuses on the origin, scope, and nature of neutral- ities. NS used in this study is norm-entropy-based, and it is called Modified Neutrosophic Set Segmentation (MNSS). 3D modeling method via MNSS (3DMM_MNSS) proposed in this study improves the quality of single object 3D modeling through an NS stratagem ca
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46

Pranab, Biswas, Pramanik Surapati, and C. Giri Bibhas. "TOPSIS method for multi-attribute group decision making under single-valued neutrosophic environment." December 6, 2013. https://doi.org/10.5281/zenodo.34915.

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A single-valued neutrosophic set is a special case of neutrosophic set. It has been proposed as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets in order to deal with incomplete information.
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47

Irfan, Deli. "Interval-valued neutrosophic soft sets and its decision making." February 23, 2014. https://doi.org/10.5281/zenodo.32261.

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In this paper, the notion of the interval valued neutrosophic soft sets (ivn−soft sets) is defined which is a combination of an interval valued neutrosophic sets [36] and a soft sets [30]. Our ivn−soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set,intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft set. Then, we introduce some definitions and operations on ivn−soft sets sets. Some properties of ivn−soft sets which are connected to operations have been e
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48

A., A. Salama, Smarandache Florentin, and Kromov Valeri. "Neutrosophic Closed Set and Neutrosophic Continuous Functions." April 16, 2014. https://doi.org/10.5281/zenodo.30213.

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In this paper, we introduce and study the concept of "neutrosophic closed set "and "neutrosophic continuous function". Possible application to GIS topology rules are touched upon.
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49

Mumtaz, Ali, and Smarandache Florentin. "A New Type of Group Action Through the Applications of Fuzzy Sets and Neutrosophic Sets." April 16, 2015. https://doi.org/10.5281/zenodo.49139.

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Fuzzy sets are the most significant tools to handle uncertain data while neutrosophic sets are the generalizations of fuzzy sets in the sense to handle uncertain, incomplete, inconsistent, indeterminate, false data. In this paper, we introduced fuzzy subspaces and neutrosophic subspaces (generalization of fuzzy subspaces) by applying group actions.Further, we define fuzzy transitivity and neutrosophic transitivty in this paper. Fuzzy orbits and neutrosophic orbits are introduced as well. We also studied some basic properties of fuzzy subspaces as well as neutrosophic subspaces.
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Das, Pintu, and Tapan Kumar Roy. "Multi-objective non-linear programming problem based on Neutrosophic Optimization Technique and its application in Riser Design Problem." Neutrosophic Sets and Systems 9, 2015 (May 4, 2015). https://doi.org/10.5281/zenodo.571480.

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Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. The paper aims to give computational algorithm to solve a multi-objective non-linear programming problem (MONLPP) using neutrosophic optimization method.
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