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Journal articles on the topic 'Neutrosophic set theory'

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

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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3

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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4

Al-Odhari, Adel. "Basic Introduction of Neutrosophic Set Theory." Plithogenic Logic and Computation 2 (July 3, 2024): 20–28. http://dx.doi.org/10.61356/j.plc.2024.2327.

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This paper is devoted to introducing the basic introduction to neutrosophic set theory. Neutrosophic laws defined by the partial algebra are totally (100%) true. We study three types of neutrosophic sets H1t[I], H2t[I] and H3t[I], and defined the notions of empty neutrosophic set, universal neutrosophic set, equality of neutrosophic set, neutrosophic subsets, complement of neutrosophic set, and their properties.

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5

Songsaeng, Metawee, and Aiyared Iampan. "Neutrosophic Set Theory Applied to UP-Algebras." European Journal of Pure and Applied Mathematics 12, no. 4 (2019): 1382–409. http://dx.doi.org/10.29020/nybg.ejpam.v12i4.3543.

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The notions of neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are introduced, and several properties are investigated. Conditions for neutrosophic sets to be neutrosophic UP-subalgebras, neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, and neutrosophic strongly UP-ideals of UP-algebras are provided. Relations between neutrosophic UP-subalgebras (resp., neutrosophic near UP-filters, neutrosophic UP-filters, neutrosophic UP-ideals, neutrosophic strongly UP

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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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7

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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8

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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9

Al-Odhari, Adel. "Some Results of Neutrosophic Relations for Neutrosophic Set Theory." Neutrosophic Knowledge 5 (November 14, 2024): 76–86. https://doi.org/10.5281/zenodo.14181753.

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<strong>Abstract:</strong> Nearly thirty years ago, the science of Neutrosophic appeared at the hands of the scientist Smarandache, who generalized the concept of the intuitionistic set to the neutrosophic set and the intuitionistic logic into the neutrosophic logic according to the degree of membership functions truth, indeterminacy, and falsehood respectively. Moreover, he presented the neutrosophic structure of a set when he studied the structure of neutrosophic algebra with other scholars in their works neutrosophic groups, and neutrosophic rings. Later, a few scholars who take the concept

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10

Al-Odhari, Adel. "Invertible Neutrosophic Functions on Neutrosophic Set Theory of Three Types." Neutrosophic Knowledge 6 (January 26, 2025): 21–29. https://doi.org/10.5281/zenodo.14740796.

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Abstract:  The aim of this paper is to present the reasons or arguments for believing that the transformation from classical set theory into neutrosophic set theory may be possible for the neutrosophic set of three types. For this reason, I present the invertible neutrosophic function, Bijective Neutrosophic function, Neutrosophic Image, investigate some examples, and prove theorems.     Keywords: Neutrosophic sets, Neutrosophic function on, Inverse Neutrosophic Function on, Neutrosophic Image; Properties of Neutrosophic Function on, Bijective 

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11

Al-Odhari, Adel Mohammed. "Neutrosophic Cosets and Neutrosophic Normal Subgroups of Neutrosophic Groups Associated With Gt1 [I]." مجلة جامعة صنعاء للعلوم التطبيقية والتكنولوجيا 3, no. 3 (2025): 848–60. https://doi.org/10.59628/jast.v3i3.1666.

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The Article discusses neutrosophic left/right cosets, their properties, neutrosophic normal subgroups, and neutrosophic quotient groups with some theories and examples. The concept of Neutrosophic Groups was introduced by Kandasamy and Smarandache in their work in 2006 as part of a broader field of research in neutrosophy. Neutrosophic Groups are defined by classical NeutroAxioms according to the Neutrosophic Set theory, which has type-1, The paper explores various structures related to Neutrosophic Groups, including examples of neutrosophic groups, neutrosophic left/right cosets, neutrosophic

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12

Iampan, Aiyared, N. Rajesh, and B. Brundha. "Neutrosophic set theory applied to Hilbert algebras Aiyared Iampan1∗,." International Journal of Neutrosophic Science 21, no. 4 (2023): 84–93. http://dx.doi.org/10.54216/ijns.210409.

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In this paper, the notions of neutrosophic subalgebras, neutrosophic ideals, and neutrosophic deductive systems of Hilbert algebras are introduced, and some related properties are investigated. Relations between the notions are given. Finally, we study the properties of homomorphism of Hilbert algebras.

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13

Voskoglou, Michael Gr. "Neutrosophic Assessment and Decision Making." EQUATIONS 3 (October 2, 2023): 68–72. http://dx.doi.org/10.37394/232021.2023.3.9.

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Smarandache’s theory of neutrosophy is a generalization of Zadeh’s fuzziness characterizing each element of the universal set with the membership degree, as in fuzzy sets, and in addition with the degrees of non-membership and indeterminacy with respect to the corresponding neutrosophic set. In the present work we use neutrosophic sets as tools for assessment and decision making. This turns out to be very useful when one is not sure about the correctness of the grades assigned to the elements of the universal set. Examples are also presented illustrating our results.

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14

Al-Quran, Ashraf, and Nasruddin Hassan. "Neutrosophic vague soft expert set theory." Journal of Intelligent & Fuzzy Systems 30, no. 6 (2016): 3691–702. http://dx.doi.org/10.3233/ifs-162118.

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15

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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16

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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17

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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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

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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20

A., A. SALAMA, and SMARANDACHE FLORENTIN. "Neutrosophic Crisp Probability Theory & Decision Making Process." December 10, 2016. https://doi.org/10.5281/zenodo.200051.

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Since the world is full of indeterminacy, the neutrosophics found their place into contemporary research. In neutrosophic set, indeterminacy is quantified explicitly and truth-membership, indeterminacy-membership and falsity-membership are independent. So it is natural to adopt for that purpose the value from the selected set with highest degree of truth-membership, indeterminacy membership and least degree of falsity-membership on the decision set. These factors indicate that a decision making process takes place in neutrosophic environment. In this paper, we introduce and study the probabili

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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

Salama, A. A., and Florentin Smarandache. "Neutrosophic Crisp Set Theory." Neutrosophic Sets and Systems 5, 2014 (May 4, 2014). https://doi.org/10.5281/zenodo.571506.

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The purpose of this paper is to introduce new types of neutrosophic crisp sets with three types 1, 2, 3. After given the fundamental definitions and operations, we obtain several properties, and discussed the relationship between neutrosophic crisp sets and others. Also, we introduce and study the neutrosophic crisp point and neutrosophic crisp relations. Possible applications to database are touched upon.

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23

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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Said, Broumi, Smarandache Florentin, and Dhar Mamoni. "Rough Neutrosophic Sets." May 3, 2013. https://doi.org/10.5281/zenodo.30310.

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Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information. In this paper we develop an hybrid structure called rough neutrosophic sets and studied their properties.

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25

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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27

Smarandache, Florentin. "Introduction to Neutrosophic Genetics." International Journal of Neutrosophic Science, 2021, 23–27. http://dx.doi.org/10.54216/ijns.130103.

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Neutrosophic Genetics is the study of genetics using neutrosophic logic, set, probability, statistics, measurement, and other neutrosophic tools and procedures. In this paper, based on the Neutrosophic Theory of Evolution (that includes degrees of Evolution, Neutrality (or Indeterminacy), and Involution) – as an extension of Darwin’s Theory of Evolution, we show the applicability of neutrosophy in genetics, and we present within the frame of neutrosophic genetics the following concepts: neutrosophic mutation, neutrosophic speciation, and neutrosophic coevolution

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28

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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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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Eman, AboElHamd, M. Shamma Hamed, Saleh Mohamed, and El-Khodary Ihab. "Neutrosophic Logic Theory and Applications." March 21, 2021. https://doi.org/10.5281/zenodo.4625674.

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  <em>Neutrosophic logic is a very powerful and effective concept. It has different application areas due to</em> <em>its ability to capture the stochasticity in many complex real-life use cases. This paper presents the main types</em> <em>of neutrosophic sets. It also surveys and analyzes its most common applications.</em>  

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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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Said, Broumi, Smarandache Florentin, and Dhar Mamoni. "ROUGH NEUTROSOPHIC SETS." September 6, 2014. https://doi.org/10.5281/zenodo.49128.

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 Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information. In this paper we develop an hybrid structure called rough neutrosophic sets and studied their properties. 

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T., Madhumathi, Nirmala Irudayam F., and Smarandache Florentin. "A Note On Neutrosophic Chaotic Continuous functions." April 6, 2019. https://doi.org/10.5281/zenodo.2631506.

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Many real time problems are based on uncertainity and chaotic environment. To demonstrate this ambiguous suitua-tion more precisely we intend to amalgamate the ideas of chaos theory and neutrosophy. Neutrosophy is a flourishing arena which conceptualizes the notions of true, falsity and indeterminacy attributes of an event. Chaos theory is another branch which brings out the concepts of periodic point, orbit and sensitive of a set. Hence in this paper we focus on the introducing the idea of chaotic periodic points, orbit sets, sensitive functions under neutrosophic settings. We start with defi

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Emad, Marei. "Single Valued Neutrosophic Soft Approach to Rough Sets, Theory and Application." April 28, 2018. https://doi.org/10.5281/zenodo.1235387.

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This paper aims to introduce a single valued neutrosophic soft approach to rough sets based on neutrosophic right minimal structure. Some of its properties are deduced and proved. A comparison between traditional rough model and suggested model, by using their properties is concluded to show that Pawlak’s approach to rough sets can be viewed as a special case of single valued neutrosophic soft approach to rough sets.

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Mehmet, Şahin, Uluçay Vakkas, and Broumi Said. "Bipolar Neutrosophic Soft Expert Set Theory." April 30, 2018. https://doi.org/10.5281/zenodo.1237874.

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In this paper, we introduce for the first time the concept of bipolar neutrosophic soft expert set and its some operations. Also, the concept of bipolar neutrosophic soft expert set and its basic operations, namely complement, union and intersection. We give examples for these concepts.

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Muhammad, Ihsan, Saeed Muhammad, and Ur Rahman Atiqe. "Neutrosophic Hypersoft Expert Set: Theory and Applications." June 29, 2022. https://doi.org/10.5281/zenodo.6774883.

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Soft set-like models deal with single argument approximate functions while hypersoft set, an extension of the soft set, deals with multi-argument approximate functions. The soft set cannot handle situations when attributes are required to be further divided into disjoint attribute-valued sets. To overcome this situation, a hypersoft set has been developed. In different fields like decision making and medical diagnosis, many researchers developed models based on the soft set for the solution of many problems. But these models deal with only one expert who creates many problems for the users, pr

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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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Xiaohong, Zhang, Mao Xiaoyan, Wu Yuntian, and Zhai Xuehuan. "NEUTROSOPHIC FILTERS IN PSEUDO-BCI ALGEBRAS." May 21, 2019. https://doi.org/10.5281/zenodo.3077461.

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The concept of the neutrosophic set was introduced by Smarandache; it is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. The notion of pseudo-BCI algebra was introduced by Dudek and Jun; it is a kind of nonclassical logic algebra and has a close connection with various noncommutative fuzzy logics. In this paper, neutrosophic set theory is applied to pseudo-BCI algebras. The new concepts of neutrosophic filter, neutrosophic normal filter, antigrouped neutrosophic filter, and neutrosophic p-filter in pseudo-BCI algebras are proposed, and their

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Bui, Cong Cuong, Hong Phong Pham, and Florentin Smarandache. "Standard Neutrosophic Soft Theory: Some First Results." Neutrosophic Sets and Systems 12, 2016 (June 15, 2016). https://doi.org/10.5281/zenodo.571149.

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The traditional soft set is a mapping from a parameter set to family of all crisp subsets of a universe. Molodtsov introduced the soft set as a generalized tool for modelling complex systems involving uncertain or not clearly defined objects. In this paper, the notion of neutrosophic soft set is reanalysed. The novel theory is a combination of neutrosophic set theory and soft set theory. The complement, “and”, “or”, intersection and union operations are defined on the neutrosophic soft sets. The neutrosophic soft relations accompanied with their compositions are also defined. The basic propert

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40

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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Mustafa, Hasan Hadi, and A.A. Al-Swidi L. "The Neutrosophic Axial Set theory." October 2, 2022. https://doi.org/10.5281/zenodo.7135299.

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We presented in this paper a new concept of sets that we launched it neutrosophic axial sets . These sets are considered as generalization of neutrosophic sets . The union relationships , intersection, union , belonging and other concepts were built on these sets , then we created two different concepts of points . Also we studied many important properties and basic theories about axial sets theory.

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Nor, Liyana Amalini Mohd Kamal, Abdullah Lazim, Abdullah Ilyani, Alkhazaleh Shawkat, and Karaaslan Faruk. "Multi-Valued Interval Neutrosophic Soft Set: Formulation and Theory." December 10, 2019. https://doi.org/10.5281/zenodo.3569679.

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Neutrosophic set is a powerful general formal framework. A lot of studies on neutrosophic had been proposed and recently, in multi-valued interval values. However, sometimes there is problem involving elements of ambiguity and uncertainties in which the function of membership is difficult to be set in a particular case. Clearly, these problems can be solved by soft set since it is able to solve the lack of parameterization tool of theory. Thus, this paper introduces a concept of multi-valued interval neutrosophic soft set which amalgamates multi-valued interval neutrosophic set and soft set. T

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Ashraf, Al-Quran, and Hassan Nasruddin. "Neutrosophic vague soft expert set theory." September 27, 2016. https://doi.org/10.5281/zenodo.236065.

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In this paper, we first introduce the concept of neutrosophic vague soft expert sets (NVSESs for short) which combines neutrosophic vague sets and soft expert sets to be more effective and useful. We also define its basic operations, namely complement, union, intersection, AND and OR along with illustrative examples, and study some related properties with supporting proofs. Lastly, this concept is applied to a decision making problem and its effectiveness is demonstrated using a hypothetical example.

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Memet, Şahin, Kargın Abdullah, and Ali Çoban Mehmet. "Fixed Point Theorem for Neutrosophic Triplet Partial Metric Space." September 10, 2018. https://doi.org/10.5281/zenodo.1412627.

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Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied. We show that both classical metric and neutrosophic triplet metric (NTM) are different from NTPM.

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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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Muhammad, Saeed, Ur Rahman Atiqe, Arshad Muhammad, and Dhital Alok. "A Novel Approach to Neutrosophic Hypersoft Graphs with Properties." October 7, 2021. https://doi.org/10.5281/zenodo.5553538.

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Neutrosophic hypersoft set is the combination of neutrosophic set and hypersoft set. It resolves the limitations of intuitionistic fuzzy sets and soft sets for the consideration of the degree of indeterminacy and multi-argument approximate function respectively. In this research article, a novel framework i.e. neutrosophic hypersoft graph, is formulated for handling neutrosophic hypersoft information by combining the concept of neutrosophic hypersoft sets with graph theory. Firstly, some of essential and fundamental notions of neutrosophic hypersoft graph are characterized with the help of num

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Shawkat, Alkhazaleh, and Marei Emad. "Mappings on Neutrosophic Soft Classes." July 1, 2015. https://doi.org/10.5281/zenodo.22563.

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In 1995 Smarandache introduced the concept of neutrosophic set which is a mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. In 2013 Maji introduced the concept of neutrosophic soft set theory as a general mathematical tool for dealing with uncertainty. In this paper we define the notion of a mapping on classes where the neutrosophic soft classes are collections of neutrosophic soft set. We also define and study the properties of neutrosophic soft images and neutrosophic soft inverse images of neutrosophic s

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Praba, B. Pooja S., and Sivakumar Nethraa. "Attribute based Double Bounded Rough Neutrosophic Sets in Facial Expression Detection." April 9, 2022. https://doi.org/10.5281/zenodo.6426416.

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In this paper, a hybrid intelligent structure called “Double Bounded Rough Neutrosophic Sets” is defined, which is a combination of Neutrosophic sets theory and Rough sets theory. Further, the Attribute based Double Bounded Rough Neutrosophic Sets was implemented using this hybrid intelligent structure for Facial Expression Detection on real time data. Facial expression detection is becoming increasingly important to understand one’s emotion automatically and efficiently and is rich in applications. This paper implements some of these applications of facial expression such as

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Anjan, Mukherjee, and Sarkar Sadhan. "A new method of measuring similarity between two neutrosophic soft sets and its application in pattern recognition problems." July 1, 2015. https://doi.org/10.5281/zenodo.21454.

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Smarandache in 1995 introduced the concept of neutrosophic set and in 2013 Maji introduced the notion of neutrosophic soft set, which is a hybridization of neutrosophic set and soft set. After its introduction neutrosophic soft sets become most efficient tools to deals with problems that contain uncertainty such as problem in social, economic system, medical diagnosis, pattern recognition, game theory, coding theory and so on. In this work a new method of measuring similarity measure and weighted similarity measure between two neutrosophic soft sets (NSSs) are proposed. A comparative study wit

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Metawee, Songsaeng, and Iampan Aiyared. "Image and Inverse Image of Neutrosophic Cubic Sets in UP-Algebras under UP-Homomorphisms." August 18, 2020. https://doi.org/10.5281/zenodo.3989433.

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The concept of a neutrosophic cubic set in a UP-algebra was introduced by Songsaeng and Iampan [Neutrosophic cubic set theory applied to UP-algebras, 2019]. In this paper, we define the image and inverse image of a neutrosophic cubic set in a non-empty set under any function and study the image and inverse image of a neutrosophic cubic UP-subalgebra (resp., neutrosophic cubic near UP-filter, neutrosophic cubic UP-filter, neutrosophic cubic UP-ideal, neutrosophic cubic strong UP-ideal) of a UP-algebra under some UP-homomorphisms. 

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