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Journal articles on the topic 'Smarandache's Neutrosophy'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Lupianez, Francisco Gallego. "On neutrosophic paraconsistent topology." Kybernetes 39, no. 4 (2010): 598–601. https://doi.org/10.1108/03684921011036817.

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Recently, F. Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets (NSs). Also, this author introduced a general definition of neutrosophic topology. On the other hand, there exist various kinds of paraconsistent logics, where some contradiction is admissible. The purpose of this paper is to show that a Smarandache's definition of neutrosophic paraconsistent topology is not a generalization of Çoker's intuitionistic fuzzy topology (IFT) or Smarandache's general neutrosophic topology.

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2

Voskoglou, Michael Gr. "From Zadeh’s Fuzziness to Smarandache’s Neutrosophy: A Review." International Journal of Applied Mathematics, Computational Science and Systems Engineering 4 (December 31, 2022): 98–104. http://dx.doi.org/10.37394/232026.2022.4.13.

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The present paper reviews the process that led from Zadeh’s fuzziness to Smarandache’s neutrosophy. Starting from fuzzy sets and logic and Atanassov’s intuitionistic fuzzy sets, it proceeds to a detailed study of the concept of neutrosophic set, which takes in account the existing in real life indeterminacy. The basic operations on neutrosophic sets are defined and the classical notion of topological space is extended to the notion of neutrosophic topological space, where fundamental properties and concepts like convergence, continuity, compactness and Hausdorff topological spaces are naturall

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3

Novak-Marcincin, Jozef, Adrian Nicolescu, and Mirela Teodorescu. "Neutrosophic Circuits of Communication - A Review." International Letters of Social and Humanistic Sciences 43 (November 2014): 174–86. http://dx.doi.org/10.18052/www.scipress.com/ilshs.43.174.

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“Communication Neutrosophic Routes” by Florentin Smarandache and Ştefan Vlăduţescu was published by Education Publishing, Ohio, USA, on May 2014. Florentin Smarandache and Ştefan Vlăduţescu are two remarcable professors, first at University of New Mexico/ USA, the second at University of Craiova/ Romania, with many researches in neutrosophical, communication, mathematic, literature, journalism, social sciencies. Neutrosophy had been in the emergence phase since 1995. With its certification by the scientific community, Neutrosophy has become a type of incident knowledge, i.e. applicable in diff

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4

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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5

Kandasamy W.B., Vasantha, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Duplets of {Zpn,×} and {Zpq,×} and Their Properties." Symmetry 10, no. 8 (2018): 345. http://dx.doi.org/10.3390/sym10080345.

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The notions of neutrosophy, neutrosophic algebraic structures, neutrosophic duplet and neutrosophic triplet were introduced by Florentin Smarandache. In this paper, the neutrosophic duplets of Z p n , Z p q and Z p 1 p 2 … p n are studied. In the case of Z p n and Z p q , the complete characterization of neutrosophic duplets are given. In the case of Z p 1 … p n , only the neutrosophic duplets associated with p i s are provided; i = 1 , 2 , … , n . Some open problems related to neutrosophic duplets are proposed.

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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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Alamin, Abdul, Aditi Biswas, Kamal Hossain Gazi, and Sankar Prasad Mondal Sankar. "Modelling with Neutrosophic Fuzzy Sets for Financial Applications in Discrete System." Spectrum of Engineering and Management Sciences 2, no. 1 (2024): 263–80. https://doi.org/10.31181/sems21202433a.

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A unique branch of philosophy known as "Neutrosophy" describes the nature, genesis and scope of neutralities. F. Smarandache originated the neutrosophic set. As an extension of the intuitionistic set, he showed the degree of indeterminacy as an independent component. The application of the neutrosophic numbers, that is, the financial applications in discrete systems is analysed here. In this research paper, we consider the two cases of the financial applications of the neutrosophic environment with its numerical illustration on the basis of fuzzy difference equations.

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8

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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9

Smarandache, Florentin, and Victor Christianto. "A few little steps beyond Knuth’s Boolean Logic Table with Neutrosophic Logic: A Paradigm Shift in Uncertain Computation." Prospects for Applied Mathematics and Data Analysis 2, no. 2 (2023): 22–26. http://dx.doi.org/10.54216/pamda.020201.

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The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indete

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10

Saber, Yaser, Fahad Alsharari, and Florentin Smarandache. "On Single-Valued Neutrosophic Ideals in Šostak Sense." Symmetry 12, no. 2 (2020): 193. http://dx.doi.org/10.3390/sym12020193.

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Neutrosophy is a recent section of philosophy. It was initiated in 1980 by Smarandache. It was presented as the study of origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. In this paper, we introduce the notion of single-valued neutrosophic ideals sets in Šostak’s sense, which is considered as a generalization of fuzzy ideals in Šostak’s sense and intuitionistic fuzzy ideals. The concept of single-valued neutrosophic ideal open local function is also introduced for a single-valued neutrosophic topological space. The basic structure, espe

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Michael, Michael, Ketty M. Moscoso .., Percy T. Avila Avila-Zanabria, Omar A. Vivanco-Nu� Vivanco-Nuñez, and Paul C. Calderon Calderon-Fernandez. "Neutrosophic Social Structures and Neutrosophic 2-tuples Technique for Studying Labor Insertion and Gender Inequality." International Journal of Neutrosophic Science 24, no. 2 (2024): 229–36. http://dx.doi.org/10.54216/ijns.240220.

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This study explores the dynamics of job placement and gender inequality at the Universidad Peruana Los Andes in Huancayo, Peru, with a focus on the application of neutrosophic methods. Recognizing the nuanced differences in professional opportunities for men and women, we employ the Smarandachean theory of neutrosophic social structures to examine these disparities. During 2021-2022, we conducted surveys among university graduates, utilizing the 2-tuple linguistic neutrosophic model to measure their satisfaction levels. This approach, grounded in neutrosophy, allows for a more precise capture

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12

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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13

Teodorescu, Mirela, and Dan Ionescu. "Florentin Smarandache & Ştefan Vlăduţescu: Neutrosophic Emergences and Incidences in Communication and Information - Book Review." International Letters of Social and Humanistic Sciences 38 (August 2014): 94–99. http://dx.doi.org/10.18052/www.scipress.com/ilshs.38.94.

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Neutrosophic emergences and incidences in communication and information, published in Germany/Saarbrücken: LAP LAMBERT Academic Publishing in 2013, is a book that constitutes a new trend, a new approach in the science of logic, philosophy, communication theory, information, an approached and exemplification that it was wanted, it was intuited, it was expected but it has no mathematical foundation, that is neutrosophy. It is a book that presents avant-garde information. It is written by two appreciated researchers and inexhaustible perpetual idea machines: Professors Florentin Smarandache and Ş

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Paraskevas, Antonios, and Michael Madas. "A Neutrosophic Model for Measuring Evolution, Involution, and Indeterminacy in Species: Integrating Common and Uncommon Traits in Environmental Adaptation." Neutrosophic Systems with Applications 23 (November 1, 2024): 23–32. http://dx.doi.org/10.61356/j.nswa.2024.23400.

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In 2017, Professor F. Smarandache introduced the Neutrosophic Theory of Evolution, Involution, and Indeterminacy (or Neutrality) (NToEIaI). He concluded that every theory of evolution is characterized by a certain degree of truth, indeterminacy, and untruth, as in neutrosophic logic. In this perspective, he raised several open questions on evolution, neutrality, and involution that required further research effort. Very recently, in 2024, Smarandache conducted research, from a soft sciences/philosophical viewpoint, on identifying and studying common parts in uncommon things and uncommon parts

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Nicolescu, Adrian, and Mirela Teodorescu. "A Unifying Field in Logics - Book Review." International Letters of Social and Humanistic Sciences 43 (November 2014): 48–59. http://dx.doi.org/10.18052/www.scipress.com/ilshs.43.48.

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Paradoxism is an avant-garde movement in literature, art, philosophy, science, based on excessive use of antitheses, antinomies, contradictions, parables, odds, paradoxes in creations. It was set up and led by the writer Florentin Smarandache since 1980's, who said: "The goal is to enlargement of the artistic sphere through non-artistic elements. But especially the counter-time, counter-sense creation. Also, to experiment." Paradoxism = paradox + ism, means the theory and school of using paradoxes in literary, artistic, philosophical, scientific creations. "Paradoxism started as an anti-totali

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16

Calefariu, Emilia, Mircea Boșcoianu, Florentin Smarandache, and Traian Alexandru Buda. "Neutrosophic Modeling of Investment Architectures." Applied Mechanics and Materials 657 (October 2014): 1011–15. http://dx.doi.org/10.4028/www.scientific.net/amm.657.1011.

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Despite numerous attempts to refocus traditional bivalent logic, usually, logic is tributary by keeping fixed limits for truth or false. An alternative answer to this need is the system of Neutrosophy, and its connected logic, Neutrosophic Logic, presented in the work of the authors W. B. Vasantha Kandasamy and Florentin Smarandache. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. We are surrounded by indeterminacy, which can be pointed in any situation that, from one point of

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17

Stănescu, Georgiana Camelia. "NEUTROSOPHIC SOCIO-DISCOURSIVENESS: FROM CEREMONIAL TO INCERTITUDE." Social Sciences and Education Research Review 9, no. 2 (2022): 175–83. https://doi.org/10.5281/zenodo.10054121.

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This study represents an implementation of neutrosophy in the field of verbal communication (discourse). The methods used include meta-analytical, comparative, and inductive techniques. In relation to the neutrosophic criterion (F. Smarandache), as well as to the way of thinking (Vattimo G & Rovatti P-A, 1998), we can distinguish two types of discourse: the ceremonial and the impositive discourse. In Gianni Vattimo's opinion (1998), there are two types of thinking: weak and strong thinking (weak and strong thought). The ceremonial discourse is based on weak thinking, and it has a high neut

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18

Lupianez, Francisco Gallego. "Interval neutrosophic sets and topology." Kybernetes 38, no. 3-4 (2009): 621–24. https://doi.org/10.1108/03684920910944849.

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In 2005, Smarandache generalized the Atanassov's intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.  

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19

Al-Odhari, Adel. "Characteristics Neutrosophic Subgroups of Axiomatic Neutrosophic Groups." Neutrosophic Optimization and Intelligent Systems 3 (May 31, 2024): 32–40. http://dx.doi.org/10.61356/j.nois.2024.3265.

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This paper aims to introduce the characteristics of neutrosophic subgroups. Neutrosophic laws defined by the partial algebra are totally (100%) true. Neutrosophic groups were introduced in 2006 by Kandasamy and Smarandache, in this paper we studied the properties of neutrosophic subgroups.

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Al-Tahan, Madeleine, Bijan Davvaz, Florentin Smarandache, and Osman Anis. "On Some NeutroHyperstructures." Symmetry 13, no. 4 (2021): 535. http://dx.doi.org/10.3390/sym13040535.

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Neutrosophy, the study of neutralities, is a new branch of Philosophy that has applications in many different fields of science. Inspired by the idea of Neutrosophy, Smarandache introduced NeutroAlgebraicStructures (or NeutroAlgebras) by allowing the partiality and indeterminacy to be included in the structures’ operations and/or axioms. The aim of this paper is to combine the concept of Neutrosophy with hyperstructures theory. In this regard, we introduce NeutroSemihypergroups as well as NeutroHv-Semigroups and study their properties by providing several illustrative examples.

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21

Shawqi, Shawqi, and Adel Al Al-Odhari. "Characteristics Neutrosophic Homomorphism for Neutrosophic Rings: On Review." Prospects for Applied Mathematics and Data Analysis 3, no. 1 (2023): 63–71. https://doi.org/10.54216/pamda.030105.

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The objective of this paper is to present and study elementary properties for concept a neutrosophic ring homomorphism and isomorphism which introduced by Florentine Smarandache in 2006. We will use a concept ring homomorphism and isomorphism in classical ring.

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22

Shawqi, Shawqi, and Adel Al Al-Odhari. "Characteristics Neutrosophic Ideals For Neutrosophic Rings: On Review." Prospects for Applied Mathematics and Data Analysis 4, no. 1 (2024): 01–13. https://doi.org/10.54216/pamda.040101.

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The main objective of this paper is to present a review study with more information on the neutrosophic Ideal, Principle Ideal, Prim Ideal, Pseudo Neutrosophic Ideal, Quotient ring, and Pseudo Quotient ring. Neutrosophic ring theory is a branch of neutrosophic Algebra which introduced by Florentin Smarandache in 2006.

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23

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

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

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Yang, Hai-Long, Yan-Ling Bao, and Zhi-Lian Guo. "Generalized interval neutrosophic rough sets and its application in multi-attribute decision making." Filomat 32, no. 1 (2018): 11–33. http://dx.doi.org/10.2298/fil1801011y.

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Neutrosophic set (NS) was originally proposed by Smarandache to handle indeterminate and inconsistent information. It is a generalization of fuzzy sets and intuitionistic fuzzy sets. Wang and Smarandache proposed interval neutrosophic sets (INS) which is a special case of NSs and would be extensively applied to resolve practical issues. In this paper, we put forward generalized interval neutrosophic rough sets based on interval neutrosophic relations by combining interval neutrosophic sets with rough sets. We explore the hybrid model through constructive approach as well as axiomatic approach.

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Yuhua, Fu, and Fu Anjie. "A Revision to Godel's Incompleteness Theorem by Neutrosophy." October 15, 2007. https://doi.org/10.5281/zenodo.809318.

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According to Smarandache’s neutrosophy, the Godel’s incompleteness theorem contains the truth, the falsehood, and the indeterminacy of a statement under consideration. It is shown in this paper that the proof of G¨odel’s incompleteness theorem is faulty, because all possible situations are not considered (such as the situation where from some axioms wrong results can be deducted, for example, from the axiom of choice the paradox of the doubling ball theorem can be deducted; and many kinds of indeterminate situations, for example, a proposition can be proved in 9999 cases, and only in 1 case it

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Vasantha, Kandasamy W.B., Kandasamy Ilanthenral, and Smarandache Florentin. "Neutrosophic Duplets." May 16, 2019. https://doi.org/10.5281/zenodo.2861960.

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Mohammad, Abobala. "Classical Homomorphisms Between Refined Neutrosophic Rings and Neutrosophic Rings." August 18, 2020. https://doi.org/10.5281/zenodo.3989599.

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Neutrosophy as a generalization of classical logic introduced by Smarandache plays an important role in algebraic studies, many neutrosophic algebraic structures were defined and studied such as neutrosophic groups, and neutrosophic fields. 

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Jozef, Novak-Marcincin, Nicolescu Adrian, and Teodorescu Mirela. "Neutrosophic circuits of communication. A review." February 5, 2015. https://doi.org/10.5281/zenodo.22976.

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“Communication Neutrosophic Routes” by Florentin Smarandache and Ştefan Vlăduţescu was published by Education Publishing, Ohio, USA, on May 2014. Florentin Smarandache and Ştefan Vlăduţescu are two remarcable professors, first at University of New Mexico/ USA, the second at University of Craiova/ Romania, with many researches in neutrosophical, communication, mathematic, literature, journalism, social sciencies. Neutrosophy had been in the emergence phase since 1995. With its certification by the scientific community, Neutrosophy has become a type of incident knowledge, i.e. applic

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Jozef, Novak-Marcincin, Nicolescu Adrian, and Teodorescu Mirela. "Neutrosophic circuits of communication. A review." February 2, 2015. https://doi.org/10.5281/zenodo.23060.

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“Communication Neutrosophic Routes” by Florentin Smarandache and Ştefan Vlăduţescu was published by Education Publishing, Ohio, USA, on May 2014. Florentin Smarandache and Ştefan Vlăduţescu are two remarcable professors, first at University of New Mexico/ USA, the second at University of Craiova/ Romania, with many researches in neutrosophical, communication, mathematic, literature, journalism, social sciencies. Neutrosophy had been in the emergence phase since 1995. With its certification by the scientific community, Neutrosophy has become a type of incident knowledge, i.e. applic

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30

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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Vasantha, W.B., Kandasamy Ilanthenral, and Smarandache Florentin. "Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings." May 15, 2019. https://doi.org/10.5281/zenodo.2837785.

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The concept of neutrosophy and indeterminacy I was introduced by Smarandache, to deal with neutralies. Since then the notions of neutrosophic rings, neutrosophic semigroups and other algebraic structures have been developed. Neutrosophic duplets and their properties were introduced by Florentin and other researchers have pursued this study.In this paper authors determine the neutrosophic duplets in neutrosophic rings of characteristic zero.

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Kandasamy, Vasantha W.B., Ilanthenral Kandasamy, and Florentin Smarandache. "Algebraic Structure of Neutrosophic Duplets in Neutrosophic Rings." Neutrosophic Sets and Systems 23 (December 10, 2018). https://doi.org/10.5281/zenodo.2154646.

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The concept of neutrosophy and indeterminacy I was introduced by Smarandache, to deal with neutralies. Since then the notions of neutrosophic rings, neutrosophic semigroups and other algebraic structures have been developed. Neutrosophic duplets and their properties were introduced by Florentin and other researchers have pursued this study. In this paper authors determine the neutrosophic duplets in neutrosophic rings of characteristic zero.

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33

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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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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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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M., K. EL GAYYAR. "Smooth Neutrosophic Preuniform Spaces." December 10, 2016. https://doi.org/10.5281/zenodo.200083.

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As a new branch of philosophy, the neutrosophy was presented by Smarandache in 1998. It was presented as the study of origin, nature, and scope of neutralities; as well as their interactions with different ideational spectra. The aim of this paper is to introduce the concepts of smooth neutrosophic preuniform space, smooth neutrosophic preuniform subspace, and smooth neutrosophic preuniform mappings. Furthermore, some properties of these concepts will be investigated.

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Arulpandy, P., and Pricilla M. Trinita. "Reduction of indeterminacy of gray-scale image in bipolar neutrosophic domain." August 31, 2019. https://doi.org/10.5281/zenodo.3382501.

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Neutrosophy is a branch of philosophy introduced by Florentin Smarandache. Neutrosophic set (NS) is the derivative of neutrosophy; it is a powerful tool to handle uncertainty. Here we applied neutrosophic set to gray scale image domain for image analysis. Several authors contributed in neutrosophic image analysis and image processing. We propose a novel approach on representation of grayscale images in bipolar neutrosophic domain (BNS). The reduction of noise in images is one of the challenging task in every field. While we transform a grayscale image into bipolar neutrosophic domain, the inde

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Fu, Yuhua, and Anjie Fu. "Neutrosophic combinatorics and its applications." August 17, 2000. https://doi.org/10.5281/zenodo.9346.

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Based on the combined method in Chinese ancient I-Ching and theory of Taiji, this paper presents the Neutrosophic combinatorics by means of the combinations of the truth, the falsehood, and the indeterminacy in Smarandache’s Neutrosophy. For the Neutrosophic combinatorics we can say that “Changes originate in the Taiji; from the Taiji come the 3 spheres.

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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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Hatip, Ahmed. "The Special Neutrosophic Functions." April 15, 2020. https://doi.org/10.5281/zenodo.3824880.

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[1] L. Zadeh, , Fuzzy sets, Inform and Control, 8, pp. 338-353, 1965. [2] K.Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, pp.87-96, 1986 [3] F.Liu, XH.Yuan, Fuzzy number intuitionistic fuzzy set, Fuzzy Syst. Math, 21(1),pp.88–91, 2007. [4] H.Wang, F.Smarandache, YQ. Zhang, R. Sunderraman, Single valued neutrosophic sets. Multispace Multi-struct 4, pp.410–413, 2010. [5] F. Smarandache, Neutrosophy. Neutrosophic Logic, Set , Probability and Statistics. American Research Press, Rehoboth, 1998. International Journal of Neutrosophic Science (IJNS) Vol. 4, No. 2, PP.

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CALEFARIU, Emilia, Mircea BOȘCOIANU, FLORENTIN SMARANDACHE, and Traian Alexandru BUDA. "Neutrosophic Modeling of Investment Architectures." April 6, 2014. https://doi.org/10.5281/zenodo.49133.

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Despite numerous attempts to refocus traditional bivalent logic, usually, logic is tributary by keeping fixed limits for truth or false. An alternative answer to this need is the system of Neutrosophy, and its connected logic, Neutrosophic Logic, presented in the work of the authors W. B. Vasantha Kandasamy and Florentin Smarandache. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra.

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CALEFARIU, Emilia, Mircea BOȘCOIANU, FLORENTIN SMARANDACHE, and Traian Alexandru BUDA. "Neutrosophic Modeling of Investment Architectures." October 8, 2014. https://doi.org/10.5281/zenodo.48911.

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 Despite numerous attempts to refocus traditional bivalent logic, usually, logic is tributary by keeping fixed limits for truth or false. An alternative answer to this need is the system of Neutrosophy, and its connected logic, Neutrosophic Logic, presented in the work of the authors W. B. Vasantha Kandasamy and Florentin Smarandache. 

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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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Madeleine, Al-Tahan, and Davvaz Bijan. "On Some Prop erties of Neutrosophic Q uadruple Hv -rings." October 4, 2020. https://doi.org/10.5281/zenodo.4065443.

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  Hyperstructure theory, an 86 years old theory, has been of great interest for many algebraists where their researches were divided in to two categories: theory and applications. On the other hand, neutrosophic theory which is the study of neutralities, was introduced and developed by F. Smarandache in 1995 as an extension of dialectics. The purpose of this paper is to study some connections between the two theories: Neutrosophy and hyperstructures. In this regard, we define neutrosophic quadruple <em>H</em><em>v</em>-rings, neutrosophic quadruple <em>H</em><em>v</em>-subrings, and neutr

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Adeleke, E. O., A. A. A. Agboola, and F. Smarandache. "Refined Neutrosophic Rings I." International Journal of Neutrosophic Science, 2020, 77–81. http://dx.doi.org/10.54216/ijns.020203.

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The notion of neutrosophic ring R(I) generated by the ring R and the indeterminacy component I was introduced for the ﬁrst time in the literature by Vasantha Kandasamy and Smarandache in.12 Since then, fur-ther studies have been carried out on neutrosophic ring, neutrosophic nearring and neutrosophic hyperring see.1, 3, 4, 6–8 Recently, Smarandache10 introduced the notion of reﬁned neutrosophic logic and neutrosophic set with the splitting of the neutrosophic components T, I, F into the form T1, T2, . . . , Tp; I1, I2, . . . , Ir; F1, F2, . . . , Fs where Ti, Ii, Fi can be made to represent di

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Abd ELhamid, A., Shimaa I. Hassan, and N. M. A. Ayad. "A Glimpse of Neutrosophic Approach Publications Relevant to a Prominent Researcher in Africa of the Decade 2010 to 2020: A Digital Vision." International Journal of Neutrosophic Science, 2021, 34–51. http://dx.doi.org/10.54216/ijns.130101.

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In recent times, with a rapid spark of scientific progress and development, new scientific approaches have been begun to emerge and widely spread in various fields. Currently, the neutrosophic approach is one of the most approaches considered as a precious modern approach. With the increasing popularity of the Neutrosophic approach, the development of this approach became a great trend of science that has its own rules and principles. The overwhelming spread of the neutrosophic approach in the late 20th century has provided a new trend into the debate and research. As well, it has offered a wo

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Smarandache, Florentin. "Neutrosophie : un cadre interdisciplinaire pour une meilleure compréhension de l'incertitude et de l'indétermination." Neutrosophic Knowledge 4 (June 10, 2024). https://doi.org/10.5281/zenodo.13629495.

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<strong>Abstract: </strong>La neutrosophie, un cadre philosophique et scientifique relativement récent introduit dans les années 1990,[1] propose une approche robuste pour comprendre et modéliser l’indétermination, la contradiction et l’incertitude. Explorons les concepts fondamentaux de la neutrosophie et quelques diverses applications à travers plusieurs disciplines, notamment les mathématiques, la physique, la sociologie, la psychologie et la biologie. <strong>Keywords: </strong>incertitude ; neutrosophie ;neutrosophication&nbs

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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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Francisco, Gallego Lupiáñez. "Another Note on Paraconsistent Neutrosophic Sets." June 14, 2017. https://doi.org/10.5281/zenodo.1041408.

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In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new definition and its relation to Smarandache’s paraconsistent neutrosophic sets.

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Lupianez, Francisco Gallego. "Another Note on Paraconsistent Neutrosophic Sets." Symmetry 2017, no. 9 (2017). https://doi.org/10.3390/sym9080140.

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In an earlier paper, we proved that Smarandache’s definition of neutrosophic paraconsistent topology is neither a generalization of Çoker’s intuitionistic fuzzy topology nor a generalization of Smarandache’s neutrosophic topology. Recently, Salama and Alblowi proposed a new definition of neutrosophic topology, that generalizes Çoker’s intuitionistic fuzzy topology. Here, we study this new definition and its relation to Smarandache’s paraconsistent neutrosophic sets.

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