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Journal articles on the topic 'Neutrosophic field'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

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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Harika, Bhurgula, K. Rajani, P. Narasimha Swamy, T. Nagaiah, and L. Bhaskar. "Neutrosophic Near Algebra Over Neutrosophic Field." International Journal of Neutrosophic Science 22, no. 1 (2023): 29–34. http://dx.doi.org/10.54216/ijns.220203.

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This piece of paper aims to learn neutrosophic near algebra and neutrosophic sub near algebra. This paper is summarized with the suitable definitions and theorems of neutrosophic near algebra and neutrosophic sub near algebra. It has also been demonstrated that the direct product of neutrosophic near algebra is a neutrosophic near algebra and the intersection of neutrosophic sub near algebra is a neutrosophic near algebra on a neutrosophic field. It also examined the union of couple of neutrosophic near algebras is a neutrosophic near algebra.

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3

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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Jameel, S. Obaid, A. Mahdi Salih, R. Adnan Jaleel, and Musaddak M. A. Zahra. "On The Neutrosophic Formula of Some Matrix Equations Derived from Data Mining Theory and Control Systems." International Journal of Neutrosophic Science 19, no. 1 (2022): 267–71. http://dx.doi.org/10.54216/ijns.190122.

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This paper is dedicated to studying the neutrosophic formula of some famous matrix equations used in theoretical data mining algorithms and control systems by using neutrosophic matrices and refined neutrosophic matrices over neutrosophic real fields. On the other hand, we concentrate on the neutrosophic formula of the Sylvester equation, and Lyapunov equation, where we study their formulas and properties in terms of theorems in the neutrosophic real number field and refined real number field. Also, we illustrate many different examples to clarify the validity of our work.

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Sert, Eser, and Ahmet Alkan. "Image Edge Detection Based on Neutrosophic Set Approach Combined with Chan–Vese Algorithm." International Journal of Pattern Recognition and Artificial Intelligence 33, no. 03 (2019): 1954008. http://dx.doi.org/10.1142/s0218001419540089.

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Since edge detection is a field of study used by various disciplines, it is of vital importance to calculate it accuretly. In addition, an edge detection algorithm may be involved in many image processing phases. A recent and contemporary approach, neutrosophy is based on neutrosophic logic, neutrosophic probability, neutrosophic set and neutrosophic statistics. This method yields better results compared to various other optimization methods. Neutrosophic Set (NS) is based on the origin, nature and scope of neutralities. In NS, problems are separated into true, false and indeterminacy subsets.

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Bera, Tuhin, and Nirmal Kumar Mahapatra. "On Neutrosophic Soft Field." International Journal of Mathematics Trends and Technology 56, no. 7 (2018): 472–94. http://dx.doi.org/10.14445/22315373/ijmtt-v56p562.

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7

Zeina, Mohamed Bisher, and Yasin Karmouta. "Introduction to Neutrosophic Stochastic Processes." Neutrosophic Sets and Systems 54 (April 11, 2023): 169–83. https://doi.org/10.5281/zenodo.7817748.

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In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡 𝐼 ; 𝐼2 = 𝐼 where both {𝜉(𝑡), 𝑡 ∈ 𝑇} and {𝜂(𝑡), 𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classica

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Abdel, Fattah keshty Nabila. "Neutrosophy in Law: "Overcoming Barriers toward Innovative Legal Solutions"." Neutrosophic Knowledge 6 (February 26, 2025): 30–37. https://doi.org/10.5281/zenodo.15009384.

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Abstract: The implementation of Neutrosophy in legal studies is a relatively new field, making its foundational body of studies somewhat limited. Nevertheless, there are some early efforts seeking to explore this interaction between modern philosophical logic and law. This research aims to study the obstacles facing the implementation of neutrosophic philosophy in the legal field and how to overcome them to ensure justice and innovative dispute resolution. Neutrosophic philosophy, which is based on the concept of neutrality and accommodating contradictions, offers a flexible approach that tran

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Kungumaraj, E., E. Lathanayagam, Utpal Saikia, et al. "Neutrosophic Topological Vector Spaces and its Properties." International Journal of Neutrosophic Science 23, no. 2 (2024): 63–76. http://dx.doi.org/10.54216/ijns.230206.

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The algebraic structures Group, Ring, Field and Vector spaces are important innovations in Mathematics. Most of the theoretical concepts of Mathematics are based on the theorems related to these algebraic structures. Initially many mathematicians developed theorems related to all these algebraic structures. In 20th century most of the researchers introduced the theorems on the algebraic structures with Fuzzy and Intuitionistic fuzzy sets. Recently in 21st century the researchers concentrated on Neutrosophic sets and introduced the algebraic structures like Neutrosophic Group, Neutrosophic Ring

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Paraskevas, Antonios. "Extended Event Calculus using Neutrosophic Logic: Method, Implementation, Analysis, Recent Progress and Future Directions." Neutrosophic Systems with Applications 14 (January 12, 2024): 38–49. http://dx.doi.org/10.61356/j.nswa.2024.116.

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Brains do not reason as digital computers do. Computers reason in clear steps with statements that are either true or false, while humans reason with vague terms of common sense. Neutrosophy is a new branch of philosophy and machine intelligence that deals with neutralities, specifically the idea of indeterminacy that is evident and experienced in our everyday lives. Indeterminacy is interpreted as everything that falls between a concept, idea, statement, declaration, etc. and its opposite. The fundamental thesis of neutrosophy is to employ neutrosophic logic, an extension of fuzzy logic, to i

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11

Romdhini, Mamika Ujianita, Ashraf Al Al-Quran, Faisal Al Al-Sharqi, Mohammad K. Tahat, and Abdalwali Lutfi. "Exploring the Algebraic Structures of Q-Complex Neutrosophic Soft Fields." International Journal of Neutrosophic Science 22, no. 4 (2023): 93–105. http://dx.doi.org/10.54216/ijns.220408.

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A field is a fundamental algebraic structure that finds extensive applications in algebra and various mathematical domains. On the other hand, a Q-complex neutrosophic soft set (Q-CNSS) is a unique hybrid model that combines the characteristics of soft sets and neutrosophic sets within a complex number framework. It utilizes the effectiveness of Q-set as a powerful tool in the domain of this particular model. In this article, we leverage this model to define fields under uncertainty. We present the Q-complex neutrosophic soft field (Q-CNSF) and examine the unique algebraic properties associate

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12

Abobala, Mohammad. "On the Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations." Journal of Mathematics 2021 (February 24, 2021): 1–5. http://dx.doi.org/10.1155/2021/5591576.

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The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

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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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Jdid, Maissam, and A. Salama. "Using the Inverse Transformation Method to Generate Random Variables that follow the Neutrosophic Uniform Probability Distribution." Journal of Neutrosophic and Fuzzy Systems 6, no. 2 (2023): 15–22. http://dx.doi.org/10.54216/jnfs.060202.

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When conducting the simulation process for any of the systems according to classical logic, we start by generating random numbers belonging to the regular probability distribution on the field [0, 1] using one of the known methods, and then we convert these random numbers into random variables that follow the probability distribution that the system to be simulated works with, the simulation process that we perform it gives specific results that do not take into account the changes that may occur in the work environment of the system, to obtain more accurate results In a previous research, we

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Ali, Mumtaz, Florentin Smarandache, and Mohsin Khan. "Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field." Mathematics 6, no. 4 (2018): 46. http://dx.doi.org/10.3390/math6040046.

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16

Bhurgula, Bhurgula, Bhurgula Harika, T. Nagaiah, L. Bhaskar, and K. Vijay Kumar. "Neutrosophic Ideal of a Near Algebra." International Journal of Neutrosophic Science 25, no. 4 (2025): 169–75. https://doi.org/10.54216/ijns.250414.

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This article introduces the idea of neutrosophic ideal of a near algebra and provides a definition and example. A few fundamental features related to this approach are also explored. We also present the topics neutrosophic near algebra homomorphism, kernel of a neutrosophic near algebra and coset of a neutrosophic ideal of a near algebra. It is been briefed with the appropriate definitions and theorems on it. It is been proved that sum of the right neutrosophic ideal of a near algebra is also a right neutrosophic ideal of a near algebra over a neutrosophic field.

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Delcea, Camelia, Adrian Domenteanu, Corina Ioanăș, Vanesa Mădălina Vargas, and Alexandra Nicoleta Ciucu-Durnoi. "Quantifying Neutrosophic Research: A Bibliometric Study." Axioms 12, no. 12 (2023): 1083. http://dx.doi.org/10.3390/axioms12121083.

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In recent years, neutrosophic theory has garnered increasing attention within scholarly circles due to its applicability in various domains. Within these domains, the field of decision-making has derived significant advantages from the progressions in neutrosophic theory. Notably, neutrosophic theory has made substantial contributions by advancing and offering a range of aggregation operators and information measures specifically designed for enhancing decision-making processes. In this context, this study aims to conduct a comprehensive bibliometric analysis of the current research landscape

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18

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

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This paper aims to explore the algebra structure of refined neutrosophic numbers. Firstly, the algebra structure of neutrosophic quadruple numbers on a general field is studied. Secondly, The addition operator ⊕ and multiplication operator ⊗ on refined neutrosophic numbers are proposed and the algebra structure is discussed. We reveal that the set of neutrosophic refined numbers with an additive operation is an abelian group and the set of neutrosophic refined numbers with a multiplication operation is a neutrosophic extended triplet group. Moreover, algorithms for solving the neutral element

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CHENG, H. D., YANHUI GUO, and YINGTAO ZHANG. "A NOVEL IMAGE SEGMENTATION APPROACH BASED ON NEUTROSOPHIC SET AND IMPROVED FUZZY C-MEANS ALGORITHM." New Mathematics and Natural Computation 07, no. 01 (2011): 155–71. http://dx.doi.org/10.1142/s1793005711001858.

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Image segmentation is an important component in image processing, pattern recognition and computer vision. Many segmentation algorithms have been proposed. However, segmentation methods for both noisy and noise-free images have not been studied in much detail. Neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interaction with different ideational spectra. However, neutrosophic set needs to be specified and clarified from a technical point of view for a given application or field to demonstrate its usefulness. In this pa

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20

Owera, Safwan, and Malath F. Alaswad. "A Study of Algebraic Curves in Neutrosophic Real Ring R(I) by Using the One-Dimensional Geometric AH-Isometry." Neutrosophic Sets and Systems 54 (April 11, 2023): 209–24. https://doi.org/10.5281/zenodo.7817819.

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The objective of this paper is to study and define some algebraic curves with neutrosophic variables in neutrosophic real field 𝑅(𝐼), where we study what are the relationships between classical algebraic curves and neutrosophic algebraic curves depending on the geometric isometry (AH-Isometry).

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21

Açikgöz, Ahu, Ferhat Esenbel, Abdulhamit Maman та Seher Zorlu. "The Neutrosophization of δ-Separation Axioms". Symmetry 17, № 2 (2025): 271. https://doi.org/10.3390/sym17020271.

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Fuzzy topology has long been celebrated for its ability to address real-world challenges in areas such as information systems and decision making. However, with ongoing technological advancements and the increasing complexity of practical requirements, the focus has gradually shifted toward neutrosophic topology, a broader and more inclusive framework than fuzzy topology. While neutrosophic topology is primarily rooted in neutrosophic open sets, other related families, including neutrosophic pre-open sets, neutrosophic semi-open sets, and neutrosophic beta-open sets, have also proven instrumen

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Celik, Mehmet, and Necati Olgun. "On The Classification of Neutrosophic Complex Inner Product Spaces." Galoitica: Journal of Mathematical Structures and Applications 2, no. 1 (2022): 29–32. http://dx.doi.org/10.54216/gjmsa.020104.

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The objective of this paper is to study the neutrosophic complex inner product spaces over neutrosophic complex field C(I). Also, it determines the necessary and sufficient condition of a neutrosophic complex vector space to be a complex inner product space by using semi module isomorphisms.

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Aslam, Muhammad, and Ali Algarni. "Analyzing the Solar Energy Data Using a New Anderson-Darling Test under Indeterminacy." International Journal of Photoenergy 2020 (December 18, 2020): 1–6. http://dx.doi.org/10.1155/2020/6662389.

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The generalization of the Anderson-Darling (AD) test under neutrosophic statistics is presented in this paper. We present the designing and operating procedure of neutrosophic Anderson-Darling when the quality of interest follows the neutrosophic normal distribution. The application of the proposed test is given using data from the renewable energy field. From the analysis of the data, it is concluded that the proposed test is effective and information to be applied when the data is recorded from the complex system in the renewable energy field.

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Gonul Bilgin, Nazmiye, Dragan Pamučar, and Muhammad Riaz. "Fermatean Neutrosophic Topological Spaces and an Application of Neutrosophic Kano Method." Symmetry 14, no. 11 (2022): 2442. http://dx.doi.org/10.3390/sym14112442.

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The main objective of this paper is to redefine the concept of Fermatean neutrosophic sets as well as to introduce topological structure on Fermatean neutrosophic sets. The idea of Fermatean neutrosophic sets is the hybrid model of Fermatean fuzzy sets and neutrosophic sets to utilize key features of these structures. Topological data analysis for indeterminate and uncertain information is a rapidly developing field. Motivated by this recent trend, the idea of Fermatean neutrosophic topology is proposed, which is an extension of neutrosophic topology and Fermatean fuzzy topology. Some fundamen

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Al-Odhari, Adel Mohammad. "The Computations of Algebraic Structure of Neutrosophic Determinants." مجلة جامعة صنعاء للعلوم التطبيقية والتكنولوجيا 2, no. 1 (2024): 41–52. http://dx.doi.org/10.59628/jast.v2i1.691.

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This paper aims to make a valuable contribution to the field of neutrosophic determinants and their properties. By utilizing neutrosophic real numbers in the form of a+bI, we provide an alternative approach to recent research on determinants conducted between 2020 and 2023. Our goal is to expand the scope of academic content being developed in the theory of neutrosophic linear algebra. Additionally, we seek to complement our work on some algebraic structures of neutrosophic matrices.

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

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

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Fujita, Takaaki. "Review of Rough Turiyam Neutrosophic Directed Graphs and Rough Pentapartitioned Neutrosophic Directed Graphs." Neutrosophic Optimization and Intelligent Systems 5 (March 4, 2025): 48–79. https://doi.org/10.61356/j.nois.2025.5500.

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Graph theory, a fundamental branch of mathematics, examines relationships between entities through the use of vertices and edges. Within this field, Uncertain Graph Theory has developed as a powerful framework to represent the uncertainties found in real world networks. Among the various uncertain graph models, Turiyam Neutrosophic Graphs and Pentapartitioned Neutrosophic Graphs are well-established. However, their extension to Directed Graphs remains relatively unexplored. To address this gap, this paper presents the concepts of the Turiyam Neutrosophic Directed Graph and the Pentapartitioned

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Concepción, Iván Pimienta, Karen Aracelly Tobar Almendariz, and Walter Vayas Valdiviezo. "Neutrosophic Evaluation of Health Promotion Programs for Resource Allocation." Neutrosophic Optimization and Intelligent Systems 1 (January 28, 2024): 57–66. http://dx.doi.org/10.61356/j.nois.2024.17689.

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The efficient allocation of resources to health promotion and disease prevention programs in the field of healthcare is a multidimensional and highly sensitive challenge that requires the simultaneous consideration of multiple criteria and objectives. In this context, neutrosophic logic emerges as a promising tool capable of addressing the inherent uncertainty and imprecision in health decision-making. This article explores the application of neutrosophic logic in decision-making regarding the allocation of resources to health promotion and disease prevention programs, taking into account a wi

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Alanaz, Mazin M., and Zakariya Yahya Algamal. "Neutrosophic exponentiated inverse Rayleigh distribution: Properties and Applications." International Journal of Neutrosophic Science 21, no. 4 (2023): 36–42. http://dx.doi.org/10.54216/ijns.210404.

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In the field of survival analysis, the exponentiated inverse Rayleigh distribution is used to simulate lifetime data practices of human. In order to describe diverse survival data with indeterminacies, this work aims to create a generalization of the traditional pattern exponentiated inverse Rayleigh distribution, referred to as the neutrosophic exponentiated inverse Rayleigh distribution (NEIRD). In particular, modeling uncertain data that is roughly positively skewed makes use of the established distribution. The key statistical characteristics of the developed NEIRD, such as the neutrosophi

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Hamidi, M., and F. Smarandache. "Single-Valued Neutro Hyper BCK-Subalgebras." Journal of Mathematics 2021 (September 22, 2021): 1–11. http://dx.doi.org/10.1155/2021/6656739.

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The purpose of this paper is to introduce the notation of single-valued neutrosophic hyper BCK-subalgebras and a novel concept of neutro hyper BCK-algebras as a generalization and alternative of hyper BCK-algebras, that have a larger applicable field. In order to realize the article’s goals, we construct single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BCK-algebras on a given nonempty set. The result of the research is the generalization of single-valued neutrosophic BCK-subalgebras and neutro BCK-algebras to single-valued neutrosophic hyper BCK-subalgebras and neutro hyper BC

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Alanaz, Mazin M., Marwah Yahya Mustafa, and Zakariya Yahya Algamal. "Neutrosophic Lindley distribution with application for Alloying Metal Melting Point." International Journal of Neutrosophic Science 21, no. 4 (2023): 65–71. http://dx.doi.org/10.54216/ijns.210407.

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In the field of survival analysis, the Lindley distribution is used to mimic methods used with human lifespan data. A variety of survival statistics with indeterminacies are intended to be characterized by the neutrosophic Lindley distribution (NLD). In example, modeling unknown data that is roughly positively skewed makes use of the established distribution. The neutrosophic survival function, neutrosophic hazard rate, and neutrosophic moments are three of the developed NLD's major statistical features that are discussed in this article. Additionally, the well-known maximum likelihood estimat

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Adebisi, Sunday Adesina, and Adetunji Patience Ajuebishi. "The Order Involving the Neutrosophic Hyperstructures, the Construction and Setting up of a Typical Neutrosophic Group." HyperSoft Set Methods in Engineering 3 (November 18, 2024): 26–31. http://dx.doi.org/10.61356/j.hsse.2025.3426.

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The concepts involving the nth-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyper-Axiom and Neutrosophic SuperHyperAlgebra have been considered and treated by Florentin Smarandache and it was actually ascertained that in general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m; n)-SuperHyperStructures). In this paper, efforts are intensified as much as possible to explicitly and clearly formulate the cardinality of the nth degree of the powe

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J., J., J. Aldring, S. John Borg, and D. Ajay. "Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application." International Journal of Neutrosophic Science 26, no. 1 (2025): 40–54. https://doi.org/10.54216/ijns.260104.

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The objective of this paper is to present a perspective of Refined Neutrosophic Vector Space (r-NVS), Sub spaces and some basic operations on Refined Neutrosophic Sets such as Algebraic sum and Algebraic product. Further some basic propositions, lemma and examples are presented. Finally an application on Refined Neutrosophic Vector Space is presented in the field of e-Commerce buyer oriented product (Smart Phones) ranking to illustrate the advantage of representing r-NVS.

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Manshath, A., E. Kungumaraj, E. Lathanayagam, et al. "Neutrosophic Integrals by Reduction Formula and Partial Fraction Methods for Indefinite Integrals." International Journal of Neutrosophic Science 23, no. 1 (2024): 08–16. http://dx.doi.org/10.54216/ijns.230101.

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Neutrosophic mathematics is a branch of mathematics that deals with ambiguity, indeterminacy, and incompleteness in mathematical objects and procedures. To account for Neutrosophic uncertainty, several mathematical concepts—including the reduction formula, partial fractions, and area finding—are extended in this field. The Neutrosophic reduction formula is a technique for summarising simpler words from a complex mathematical expression when the coefficientss a ndor values may be ambiguous or unknown. By taking the potential of insufficient information into account, expands the traditional redu

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Raghav, Yashpal Singh. "Neutrosophic Generalized Exponential Robust Ratio Type Estimators." International Journal of Analysis and Applications 21 (May 1, 2023): 41. http://dx.doi.org/10.28924/2291-8639-21-2023-41.

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Estimators proposed under classical statistics fail if data are vague or indeterminate. Neutrosophic Statistics are the only alternative because its deal with indeterminacy. Extensive reserch has been conducted in this field because of its wide applicability. This study aimed to further develop the theory of neutosophic simple random sampling without replacement. In this study, a generalized neutrosophic exponential robust ratio-type estimator was proposed, and five of its member neutrosophic estimators were developed. Derivations of the bias and Mean Square Error were provided up to the first

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Dadaş, Hasanş. "Advanced Decision-Making Techniques with Generalized Close Sets in Neutrosophic Soft Bitopological Spaces." Galoitica: Journal of Mathematical Structures and Applications 10, no. 1 (2024): 08–16. http://dx.doi.org/10.54216/gjmsa.0100101.

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In recent years, neutrosophic soft bitopological spaces have emerged as a promising framework for handling uncertainty and imprecision in various domains, particularly in the context of decision-making problems. This paper presents a comprehensive study of advanced decision-making techniques using generalized close sets in neutrosophic soft bitopological spaces. The primary objective of this research is to develop a better understanding of the theoretical underpinnings of generalized close sets and their practical applications in decision-making under uncertain conditions. We begin by providin

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Jdid, Maissam. "An Efficient Neutrosophic Method for Generating Random Variates from Erlang Distribution." Neutrosophic Optimization and Intelligent Systems 2 (April 8, 2024): 56–68. http://dx.doi.org/10.61356/j.nois.2024.2218.

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The simulation process depends on generating a series of random numbers subject to a regular probability distribution in the field [0, 1]. The generation of these numbers is based on the cumulative distribution function of the regular distribution, but we encounter many systems that do not, by nature, follow the regular distribution adopted in the simulation process. Therefore, it is necessary to Convert these random numbers into random variables that follow the probability distribution in which the system to be simulated operates. In classical logic, many techniques can be used in the convers

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Fujita, Takaaki, and Florentin Smarandache. "Antipodal Turiyam Neutrosophic Graphs." Neutrosophic Optimization and Intelligent Systems 5 (November 17, 2024): 1–13. http://dx.doi.org/10.61356/j.nois.2025.5422.

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Graph theory, a mathematical field, investigates the relationships between entities through vertices and edges [29]. Within this discipline, Uncertain Graph Theory emerges to model uncertainties in realworld networks. This paper presents the concept of the Antipodal Turiyam Neutrosophic Graph. In an Antipodal Graph, two nodes are connected if their shortest path distance equals the graph's diameter, emphasizing connections between the farthest nodes. Turiyam Neutrosophic Graphs extend traditional graphs by introducing four membership values-truth, indeterminacy, falsity, and liberal state-assi

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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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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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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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Mumtaz, Ali, Florentin Smarandache, Muhammad Shabir, and Munazza Naz. "Soft Neutrosophic Ring and Soft Neutrosophic Field." Neutrosophic Sets and Systems 3, 2014 (May 5, 2014). https://doi.org/10.5281/zenodo.571748.

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In this paper, we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring. We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper we gave soft neutrosophic ring homomorphism.

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Mumtaz, Ali, Smarandache Florentin, Shabir Muhammad, and Naz Munazza. "Soft Nuetrosophic Ring and Soft Neutrosophic Field." March 3, 2014. https://doi.org/10.5281/zenodo.30325.

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Agboola, A.A.A., and S.A. Akinleye. "Neutrosophic Vector Spaces." July 1, 2015. https://doi.org/10.5281/zenodo.22603.

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The objective of this paper is to study neutrosophic vector spaces. Some basic definitions and properties of the classical vector spaces are generalized. It is shown that every neutrosophic vector space over a neutrosophic field (resp. a field) is a vector space. Also, it is shown that an element of a neutrosophic vector space over a neutrosophic field can be infinitely expressed as a linear combination of some elements of the neutrosophic vector space. Neutrosophic quotient spaces and neutrosophic vector space homomorphism are also studied.

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Mumtaz, Ali, Smarandache Florentin, and Khan Mohsin. "Study on the Development of Neutrosophic Triplet Ring and Neutrosophic Triplet Field." September 7, 2018. https://doi.org/10.5281/zenodo.1411300.

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Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field. We introduce a neutrosophic triplet ring and study some of its basic properties. Further, we define the zero divisor, neutrosophic triplet subring, neutrosophic triplet ideal, nilpotent integral neutrosophic triplet domain, and neutrosophic triplet ring homomorphism. Finally, we introduce a neutrosophic triplet field.

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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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Ali, Mumtaz, and M. Khan. "Study on the development of neutrosophic triplet ring and neutrosophic triplet field." January 8, 2014. https://doi.org/10.5281/zenodo.234094.

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Mónica, Isabel Mora Verdezoto, Antoni Teran Vaca Caludio, Ros Álvarez Deinier, and Vega Falcón Vladimir. "Neutrosophic Evaluation of Legal Strategies for Decision-making in a Digital Context." December 1, 2023. https://doi.org/10.5281/zenodo.10436871.

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The present study focused on the protection of intellectual property rights in the digital era. A methodology incorporating neutrosophy was applied to evaluate and compare different proposed legal alternatives. The inherent complexity of legal issues, characterized by ambiguous facts and diverse perspectives, underscored the relevance of neutrosophy in this field. The ELECTRE I method was adapted to a neutrosophic structure by incorporating bipolar neutrosophic numbers to manage uncertainty and ambiguity in decision-making. The final results revealed a strong preference for the "Legal Educatio

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Smarandache, Florentin. "A Unifying Field in Logics: Neutrosophic Logic. Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Set. (second version." July 12, 2000. https://doi.org/10.5281/zenodo.57658.

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The subsets T, I, F are not necessarily intervals, but may be any real subsets: discrete or continuous; single-element, finite, or (either countably or uncountably) infinite; union or intersection of various subsets; etc.

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Florentin, Smarandache, and Ali Mumtaz. "Neutrosophic Triplet Group (revisited)." June 12, 2019. https://doi.org/10.5281/zenodo.3244162.

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We have introduced for the first time the notion of neutrosophic triplet since 2014, which has the form (x, neut(x), anti(x)) with respect to a given binary well-defined law, where neut(x) is the neutral of x, and anti(x) is the opposite of x. Then we define the neutrosophic triplet group (2016), prove several theorems about it, and give some examples. This paper is an improvement and a development of our 2016 published paper. Groups are the most fundamental and rich algebraic structure with respect to some binary operation in the study of algebra. In this paper, for the first time, we introdu

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