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Journal articles on the topic 'Neutrosophic'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

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 different fields. Neutrosophy legitimating was achieved by developing some doctoral research, through learning theory as a way of description, explanation and forecast and implementation of neutrosophic congress and conferences. Neutrosophy handles all neutralities. In the neutrosophic taxonometry, a class of neutralities is represented by the neutralities that, without turning into contradiction, generate qualitative leaps. The emergence is the cognitive phenomenon in which, from two or more connected neutralities, without contradiction, a change of quality or a qualitative leap result. Thinking in Hegelian terms has an axiom the idea that the qualitative change, qualitative emergences may arise from related neutral items. Neutrosophy claims that qualitative emergences may arise from related neutral items.

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2

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

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In this article, new generalised neutrosophic soft open known as neutrosophic soft ∗ b open set is introduced in neutrosophic soft topological spaces. Neutrosophic soft ∗ b open set is generated with the help of neutrosophic soft semiopen and neutrosophic soft preopen sets. Then, with the application of this new definition, some soft neutrosophical separation axioms, countability theorems, and countable space can be Hausdorff space under the subjection of neutrosophic soft sequence which is convergent, the cardinality of neutrosophic soft countable space, engagement of neutrosophic soft countable and uncountable spaces, neutrosophic soft topological features of the various spaces, soft neutrosophical continuity, the product of different soft neutrosophical spaces, and neutrosophic soft countably compact that has the characteristics of Bolzano Weierstrass Property (BVP) are studied. In addition to this, BVP shifting from one space to another through neutrosophic soft continuous functions, neutrosophic soft sequence convergence, and its marriage with neutrosophic soft compact space, sequentially compactness are addressed.

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Et. al., N. Moogambigai. "Z-open sets in a Neutrosophic Topological Spaces." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1S (April 11, 2021): 357–62. http://dx.doi.org/10.17762/turcomat.v12i1s.1850.

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

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4

Kandasamy W.B., Vasantha, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Duplets of {Zpn,×} and {Zpq,×} and Their Properties." Symmetry 10, no. 8 (August 17, 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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5

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 (November 15, 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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6

Saber, Yaser, Fahad Alsharari, and Florentin Smarandache. "On Single-Valued Neutrosophic Ideals in Šostak Sense." Symmetry 12, no. 2 (January 25, 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, especially a basis for such generated single-valued neutrosophic topologies and several relations between different single-valued neutrosophic ideals and single-valued neutrosophic topologies, are also studied here. Finally, for the purpose of symmetry, we also define the so-called single-valued neutrosophic relations.

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7

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

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Neutrosophy deals with neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalization of the classical set, fuzzy set, and intuitionistic fuzzy set. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena, where it is necessary to study the relationship between two probability functions. In this study, the concept of an orthogonal neutrosophic metric space is initiated. It is a generalization of the neutrosophic metric space. Some fixed point results are investigated in this setting. For the validity of the obtained results, some nontrivial examples are given.

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8

Şahin, Memet, and Abdullah Kargın. "Neutrosophic Triplet v-Generalized Metric Space." Axioms 7, no. 3 (September 6, 2018): 67. http://dx.doi.org/10.3390/axioms7030067.

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The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v‐generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v‐generalized metric space (NTVGM), and we obtained properties of NTVGM. Also, we showed that NTVGM is different from the classical metric and neutrosophic triplet metric (NTM). Furthermore, we introduced completeness of NTVGM.

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9

Smarandache, Florentin. "Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set." Mathematics 7, no. 4 (April 16, 2019): 353. http://dx.doi.org/10.3390/math7040353.

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In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.

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10

CHENG, H. D., and YANHUI GUO. "A NEW NEUTROSOPHIC APPROACH TO IMAGE THRESHOLDING." New Mathematics and Natural Computation 04, no. 03 (November 2008): 291–308. http://dx.doi.org/10.1142/s1793005708001082.

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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. The neutrosophic set is a powerful general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. We apply the neutrosophic set in image domain and define some concepts and operations for image thresholding. The image G is transformed into Ns domain, which is described using three subsets T, I and F. The entropy in neutrosophic set is defined and employed to evaluate the indetermination. A new λ-mean operation is proposed to reduce the set's indetermination. Finally, the proposed method is employed to perform image thresholding. We have conducted experiments on a variety of images. The experimental results demonstrate that the proposed approach can select the thresholds automatically and effectively. Especially, it can process the "clean" images, the images with different kinds of noise and the images with multiple kinds of noise well without knowing the type of the noise, which is the most difficult task for image thresholding.

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GUO, YANHUI, H. D. CHENG, and YINGTAO ZHANG. "A NEW NEUTROSOPHIC APPROACH TO IMAGE DENOISING." New Mathematics and Natural Computation 05, no. 03 (November 2009): 653–62. http://dx.doi.org/10.1142/s1793005709001490.

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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. The neutrosophic set is a general formal framework that has been recently proposed. However, the neutrosophic set needs to be specified from a technical point of view. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. The image G is transformed into NS domain, which is described using three membership sets: T, I and F. The entropy of the neutrosophic set is defined and employed to evaluate the indeterminancy. A new operation, γ-median-filtering operation, is proposed to decrease the set indeterminancy and remove noise. We have conducted experiments on a variety of noisy images using different types of noises with different levels. The experimental results demonstrate that the proposed approach can remove noise automatically and effectively. Especially, it can process not only noisy images with different levels of noise, but also images with different kinds of noise well without knowing the type of the noise, which is the most difficult task for image denoising.

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12

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 view can be considered true, and from another point of view can be considered false. In Neutrosophic logic, every statement includes a percentage of truth (T), includes a percentage of indeterminacy (I) and a percentage of falsity (F). The major novelty of the work is that investment process is analyzed through the method of Neutrosophic logic, taking into account investment parameters such as: economic return on investment, recovery duration on investment, the resources involved (financial, human and time), the production capacity, the period of execution, the work volume, the market demand, the training of the personnel, etc. Thus, this paper consists of the analysis of interdependence and indeterminacy of these parameters. The model will be calibrated by conducting case studies, with real parameters of input to be analyzed and known output data, which will be used for the research of a present investment process.

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13

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 (February 19, 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. It helps solve indeterminate situations effectively. It has recently been used in the field of image processing as indeterminate situations are also encountered in this field. Chan–Vese (CV) model is one of the successful region-based segmentation methods. The present study proposes a new NS-based edge detection method using CV algorithm. The proposed method combines the philosophical view of NS with successful segmentation characteristics of CV model. Obtained edge detection results are compared with different edge detection methods. The performances of each method are analyzed by using Figure of Merit (FOM) and Peak Signal-To-Noise Ratio (PSNR). The results suggest that the proposed method displays a better performance assessment compared to the used well-known methods.

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14

Kandasamy W. B., Vasantha, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Triplets in Neutrosophic Rings." Mathematics 7, no. 6 (June 20, 2019): 563. http://dx.doi.org/10.3390/math7060563.

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The neutrosophic triplets in neutrosophic rings ⟨ Q ∪ I ⟩ and ⟨ R ∪ I ⟩ are investigated in this paper. However, non-trivial neutrosophic triplets are not found in ⟨ Z ∪ I ⟩ . In the neutrosophic ring of integers Z ∖ { 0 , 1 } , no element has inverse in Z. It is proved that these rings can contain only three types of neutrosophic triplets, these collections are distinct, and these collections form a torsion free abelian group as triplets under component wise product. However, these collections are not even closed under component wise addition.

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15

Mohan, J., V. Krishnaveni, and Yanhui Guo. "A New Neutrosophic Approach of Wiener Filtering for MRI Denoising." Measurement Science Review 13, no. 4 (August 1, 2013): 177–86. http://dx.doi.org/10.2478/msr-2013-0027.

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In this paper, a new filtering method based on neutrosophic set (NS) approach of wiener filter is presented to remove Rician noise from magnetic resonance image. A neutrosophic set, a part of neutrosophy theory, studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. Now, we apply the neutrosophic set into image domain and define some concepts and operators for image denoising. The image is transformed into NS domain, described using three membership sets: True (T), Indeterminacy (I) and False (F). The entropy of the neutrosophic set is defined and employed to measure the indeterminacy. The ω-wiener filtering operation is used on T and F to decrease the set indeterminacy and remove noise. The experiments have conducted on simulated Magnetic Resonance images (MRI) from Brainweb database and clinical MR images corrupted by Rician noise. The results show that the NS wiener filter produces better denoising results in terms of visual perception, qualitative and quantitative measures compared with other denoising methods, such as classical wiener filter, the anisotropic diffusion filter, the total variation minimization scheme and non local means filter.

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Smarandache, Florentin, Xiaohong Zhang, and Mumtaz Ali. "Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets." Symmetry 11, no. 2 (February 1, 2019): 171. http://dx.doi.org/10.3390/sym11020171.

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Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity (i.e. element, concept, idea, theory, logical proposition, etc.), <antiA> is the opposite of <A>, while <neutA> is the neutral (or indeterminate) between them, i.e., neither <A> nor <antiA> [...]

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17

Songsaeng, Metawee, and Aiyared Iampan. "Neutrosophic Set Theory Applied to UP-Algebras." European Journal of Pure and Applied Mathematics 12, no. 4 (October 31, 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-ideals) and their level subsets are considered.

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18

Parimala, Mani, Ranganathan Jeevitha, Saeid Jafari, Florentin Smarandache, and Ramalingam Udhayakumar. "Neutrosophic αψ-Homeomorphism in Neutrosophic Topological Spaces." Information 9, no. 8 (July 26, 2018): 187. http://dx.doi.org/10.3390/info9080187.

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In this article, the concept of neutrosophic homeomorphism and neutrosophic αψ homeomorphism in neutrosophic topological spaces is introduced. Further, the work is extended as neutrosophic αψ∗ homeomorphism, neutrosophic αψ open and closed mapping and neutrosophic Tαψ space in neutrosophic topological spaces and establishes some of their related attributes.

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Acikgoz, Ahu, and Ferhat Esenbel. "Neutrosophic soft δ-topology and neutrosophic soft δ-compactness." Filomat 34, no. 10 (2020): 3441–58. http://dx.doi.org/10.2298/fil2010441a.

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We introduce the concepts of neutrosophic soft ?-interior, neutrosophic soft quasi-coincidence, neutrosophic soft q-neighbourhood, neutrosophic soft regular open set, neutrosophic soft ?-closure, neutrosophic soft ?-closure and neutrosophic soft semi open set. It is also shown that the set of all neutrosophic soft ?-open sets is a neutrosophic soft topology, which is called the neutrosophic soft ?-topology. We obtain equivalent forms of neutrosophic soft ?-continuity. Moreover, the notions of neutrosophic soft ?-compactness and neutrosophic soft locally ?-compactness are defined and their basic properties under neutrosophic soft ?-continuous mappings are investigated.

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Hu, Qingqing, and Xiaohong Zhang. "Neutrosophic Triangular Norms and Their Derived Residuated Lattices." Symmetry 11, no. 6 (June 20, 2019): 817. http://dx.doi.org/10.3390/sym11060817.

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Neutrosophic triangular norms (t-norms) and their residuated lattices are not only the main research object of neutrosophic set theory, but also the core content of neutrosophic logic. Neutrosophic implications are important operators of neutrosophic logic. Neutrosophic residual implications based on neutrosophic t-norms can be applied to the fields of neutrosophic inference and neutrosophic control. In this paper, neutrosophic t-norms, neutrosophic residual implications, and the residuated lattices derived from neutrosophic t-norms are investigated deeply. First of all, the lattice and its corresponding system are proved to be a complete lattice and a De Morgan algebra, respectively. Second, the notions of neutrosophic t-norms are introduced on the complete lattice discussed earlier. The basic concepts and typical examples of representable and non-representable neutrosophic t-norms are obtained. Naturally, De Morgan neutrosophic triples are defined for the duality of neutrosophic t-norms and neutrosophic t-conorms with respect to neutrosophic negators. Third, neutrosophic residual implications generated from neutrosophic t-norms and their basic properties are investigated. Furthermore, residual neutrosophic t-norms are proved to be infinitely ∨-distributive, and then some important properties possessed by neutrosophic residual implications are given. Finally, a method for producing neutrosophic t-norms from neutrosophic implications is presented, and the residuated lattices are constructed on the basis of neutrosophic t-norms and neutrosophic residual implications.

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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 (March 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 paper, we apply neutrosophic set and define some operations. Neutrosphic set is integrated with an improved fuzzy c-means method and employed for image segmentation. A new operation, α-mean operation, is proposed to reduce the set indeterminacy. An improved fuzzy c-means (IFCM) is proposed based on neutrosophic set. The computation of membership and the convergence criterion of clustering are redefined accordingly. We have conducted experiments on a variety of images. The experimental results demonstrate that the proposed approach can segment images accurately and effectively. Especially, it can segment the clean images and the images having different gray levels and complex objects, which is the most difficult task for image segmentation.

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Mishra, Kritika, Ilanthenral Kandasamy, Vasantha Kandasamy W. B., and Florentin Smarandache. "A Novel Framework Using Neutrosophy for Integrated Speech and Text Sentiment Analysis." Symmetry 12, no. 10 (October 18, 2020): 1715. http://dx.doi.org/10.3390/sym12101715.

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With increasing data on the Internet, it is becoming difficult to analyze every bit and make sure it can be used efficiently for all the businesses. One useful technique using Natural Language Processing (NLP) is sentiment analysis. Various algorithms can be used to classify textual data based on various scales ranging from just positive-negative, positive-neutral-negative to a wide spectrum of emotions. While a lot of work has been done on text, only a lesser amount of research has been done on audio datasets. An audio file contains more features that can be extracted from its amplitude and frequency than a plain text file. The neutrosophic set is symmetric in nature, and similarly refined neutrosophic set that has the refined indeterminacies I1 and I2 in the middle between the extremes Truth T and False F. Neutrosophy which deals with the concept of indeterminacy is another not so explored topic in NLP. Though neutrosophy has been used in sentiment analysis of textual data, it has not been used in speech sentiment analysis. We have proposed a novel framework that performs sentiment analysis on audio files by calculating their Single-Valued Neutrosophic Sets (SVNS) and clustering them into positive-neutral-negative and combines these results with those obtained by performing sentiment analysis on the text files of those audio.

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A.A.Salama, A. A. Salama. "Neutrosophic Set and Neutrosophic Topological Spaces." IOSR Journal of Mathematics 3, no. 4 (2012): 31–35. http://dx.doi.org/10.9790/5728-0343135.

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Vasu, M., and D. Ramesh Kumar. "NEUTROSOPHIC IDEALS OF NEUTROSOPHIC BCH-ALGEBRAS." Advances in Mathematics: Scientific Journal 9, no. 11 (November 6, 2020): 9719–25. http://dx.doi.org/10.37418/amsj.9.11.79.

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ÇEVEN, Yilmaz, and Doğukan OZAN. "Neutrosophic triplets in some neutrosophic rings." Cumhuriyet Science Journal 41, no. 3 (September 30, 2020): 612–16. http://dx.doi.org/10.17776/csj.685154.

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Smarandache, Florentin. "Operators on Single-Valued Neutrosophic Oversets, Neutrosophic Undersets, and Neutrosophic Offsets." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 35e, no. 2 (2016): 53. http://dx.doi.org/10.5958/2320-3226.2016.00007.2.

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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-totalitarian protest against a closed society, Romania of 1980's, where the whole culture was manipulated by a small group. Only their ideas and their publications counted. We couldn't publish almost anything. Later, I based it on contradictions. Why? Because we lived in that society a double life: an official one - propagated by the political system, and another one real. In mass-media it was promulgated that 'our life is wonderful', but in reality 'our life was miserable'. The paradox flourishing!” (Florentin Smarandache). The new theory generalizes the fuzzy logic and introduces also two new concepts: “neutrosophy”, the study of neutralities as an extension of dialectics and its derivative “neutrosophic”, such as “neutrosophic logic”, neutrosophic set”, “neutrosophic probability”, and “neutrosophic statistics” opening in this manner ways of research in four fields: philosophy, logics, set theory and probability/statistics. According to this new theory is also available Albers Einstein’s statement: “Not everything that can be controled counts and not everything that counts can be counted “

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Takallo, M. Mohseni, Rajab Ali Borzooei, Seok-Zun Song, and Young Bae Jun. "Implicative ideals of BCK-algebras based on MBJ-neutrosophic sets." AIMS Mathematics 6, no. 10 (2021): 11029–45. http://dx.doi.org/10.3934/math.2021640.

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<abstract><p>The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established. Conditions for MBJ-neutrosophic subalgebra (resp., MBJ-neutrosophic ideal, positive implicative MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal) to be implicative MBJ-neutrosophic ideal are provided. Characterizations of implicative MBJ-neutrosophic ideal are discussed.</p></abstract>

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Jun, Young Bae, and Eun Hwan Roh. "MBJ-neutrosophic ideals of BCK/BCI-algebras." Open Mathematics 17, no. 1 (November 28, 2019): 588–601. http://dx.doi.org/10.1515/math-2019-0106.

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Abstract The notion of MBJ-neutrosophic ideal is introduced, and its properties are investigated. Conditions for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal are provided. In a BCK/BCI-algebra, a condition for an MBJ-neutrosophic set to be an MBJ-neutrosophic ideal is given. In a BCK-algebra, a condition for an MBJ-neutrosophic subalgebra to be an MBJ-neutrosophic ideal is given. In a BCI-algebra, conditions for an MBJ-neutrosophic ideal to be an MBJ-neutrosophic subalgebra are considered. In an (S)-BCK-algebra, we show that every MBJ-neutrosophic ideal is an MBJ-neutrosophic ∘-subalgebra, and a characterization of an MBJ-neutrosophic ideal is established.

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30

Abu-Saleem, M. "A neutrosophic folding and retraction on a single-valued neutrosophic graph." Journal of Intelligent & Fuzzy Systems 40, no. 3 (March 2, 2021): 5207–13. http://dx.doi.org/10.3233/jifs-201957.

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The main aim of this article is to present neutrosophic folding and neutrosophic retractions on a single-valued neutrosophic graph Ğ from the viewpoint of geometry and topology. For this reason, we use a sequence of neutrosophic transformations on Ğ to obtain a new single-valued neutrosophic graph G ˇ 1 which contains different parameters under new conditions. We deduce the isometric neutrosophic folding on neutrosophic spheres and neutrosophic torii. Also, we determine the relationship between the limit neutrosophic folding and the limit of neutrosophic retraction on Ğ. Theorems regulating these relations are attained.

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31

Gündüz, Aras, and Sadi Bayramov. "Neutrosophic soft continuity in neutrosophic soft topological spaces." Filomat 34, no. 10 (2020): 3495–506. http://dx.doi.org/10.2298/fil2010495g.

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In this study, using a more appreciate definition of a neutrosophic soft point, we introduce neutrosophic soft functions, and present the concepts of neutrosophic soft continuous, neutrosophic soft open, neutrosophic soft closed, and neutrosophic soft homeomorphic functions in a very different way from the source existing in the literature. In the investigation we prove theorems related to these concepts and provide some examples.

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32

R, Princy, and Mohana K. "Neutrosophic bipolar vague resolvable and neutrosophic bipolar vague irresolvable spaces." Journal of Computational Mathematica 5, no. 1 (June 18, 2021): 76–87. http://dx.doi.org/10.26524/cm94.

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In this paper the concepts of neutrosophic bipolar vague resolvable, neutrosophic bipolar vague irresolvable, neutrosophic bipolar vague open hereditarily irresolvable spaces, maximally neutrosophic bipolar vague irresolvable spaces and neutrosophic bipolar vague submaximal spaces are introduced. Also we study several interesting properties of the neutrosophic bipolar vague open hereditarily irresolvable spaces besides giving characterization of these spaces by means of somewhat neutrosophic bipolar vague continuous and somewhat neutrosophic bipolar vague open functions

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33

Alsubie, Abdelaziz, Anas Al-Masarwah, Young Bae Jun, and Abd Ghafur Ahmad. "An Approach to BMBJ-Neutrosophic Hyper-BCK-Ideals of Hyper-BCK-Algebras." Journal of Mathematics 2021 (May 24, 2021): 1–10. http://dx.doi.org/10.1155/2021/5552060.

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In this article, a new idea of BMBJ-neutrosophic hyper-BCK-algebras is introduced and some of its properties are investigated. Here, BMBJ-neutrosophic hyper-BCK-ideal, BMBJ-neutrosophic weak hyper-BCK-ideal, BMBJ-neutrosophic s-weak hyper-BCK-ideal, and BMBJ-neutrosophic strong hyper-BCK-ideal are presented, and some relevant results and relations are indicated. Characterizations of BMBJ-neutrosophic (weak, s-weak, strong) hyper-BCK-ideal are considered. Conditions for a BMBJ-neutrosophic weak hyper-BCK-ideal to be a BMBJ-neutrosophic s-weak hyper-BCK-ideal are provided. Conditions for an MBJ-neutrosophic set to be a BMBJ-neutrosophic strong hyper-BCK-ideal are given.

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34

Basumatary, Bhimraj, Nijwm Wary, Dimacha Dwibrang Mwchahary, Ashoke Kumar Brahma, Jwngsar Moshahary, Usha Rani Basumatary, and Jili Basumatary. "A Study on Some Properties of Neutrosophic Multi Topological Group." Symmetry 13, no. 9 (September 13, 2021): 1689. http://dx.doi.org/10.3390/sym13091689.

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In this paper, we studied some properties of the neutrosophic multi topological group. For this, we introduced the definition of semi-open neutrosophic multiset, semi-closed neutrosophic multiset, neutrosophic multi regularly open set, neutrosophic multi regularly closed set, neutrosophic multi continuous mapping, and then studied the definition of a neutrosophic multi topological group and some of their properties. Moreover, since the concept of the almost topological group is very new, we introduced the definition of neutrosophic multi almost topological group. Finally, for the purpose of symmetry, we used the definition of neutrosophic multi almost continuous mapping to define neutrosophic multi almost topological group and study some of its properties.

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35

Al-Omeri, Wadei, and Saeid Jafari. "On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces." Mathematics 7, no. 1 (December 20, 2018): 1. http://dx.doi.org/10.3390/math7010001.

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In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic p T 1 2 space and neutrosophic g p T 1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.

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36

Salama, A. A., Said Broumi, and Florentin Smarandache. "Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals." International Journal of Information Engineering and Electronic Business 6, no. 3 (June 8, 2014): 1–8. http://dx.doi.org/10.5815/ijieeb.2014.03.01.

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37

Alsharari, Fahad. "On Single-Valued Neutrosophic Closure Spaces." Symmetry 13, no. 8 (August 17, 2021): 1508. http://dx.doi.org/10.3390/sym13081508.

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This paper aims to mark out new terms of single-valued neutrosophic notions in a Šostak sense called single-valued neutrosophic semi-closure spaces. To achieve this, notions such as β£-closure operators and β£-interior operators are first defined. More precisely, these proposed contributions involve different terms of single-valued neutrosophic continuous mappings called single-valued neutrosophic (almost β£, faintly β£, weakly β£) and β£-continuous. Finally, for the purpose of symmetry, we define the single-valued neutrosophic upper, single-valued neutrosophic lower and single-valued neutrosophic boundary sets of a rough single-valued neutrosophic set αn in a single-valued neutrosophic approximation space (F˜,δ). Based on αn and δ, we also introduce the single-valued neutrosophic approximation interior operator intαnδ and the single-valued neutrosophic approximation closure operator Clαnδ.

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38

Et. al., A. Vadivel. "Neutrosophic e-Continuous Maps and Neutrosophic e-Irresolute Maps." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 1S (April 11, 2021): 369–75. http://dx.doi.org/10.17762/turcomat.v12i1s.1858.

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Aim of this present paper is to introduce and investigate new kind of neutrosophic continuous function called neutrosophic econtinuous maps in neutrosophic topological spaces and also relate with their near continuous maps. Also, a new irresolute map called neutrosophic e-irresolute maps in neutrosophic topological spaces is introduced. Further, discussed about some properties and characterization of neutrosophic e-irresolute maps in neutrosophic topological spaces.

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39

Bal, Mikail, and Necati Olgun. "Soft Neutrosophic Modules." Mathematics 6, no. 12 (December 12, 2018): 323. http://dx.doi.org/10.3390/math6120323.

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In this study, for the first time, we study some basic definitions of soft neutrosophic modules in algebra being generalized and its several related properties, structural characteristics are investigated with suitable examples. In this paper, we utilized neutrosophic soft sets and neutrosophic modules. As a result, we defined soft neutrosophic modules. After weak soft neutrosophic modules and strong soft neutrosophic modules are described and illustrated by examples. Finally soft neutrosophic module homomorphism is defined and soft neutrosophic module isomorphism is explained.

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40

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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41

Taş, Ferhat, Selçuk Topal, and Florentin Smarandache. "Clustering Neutrosophic Data Sets and Neutrosophic Valued Metric Spaces." Symmetry 10, no. 10 (September 24, 2018): 430. http://dx.doi.org/10.3390/sym10100430.

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In this paper, we define the neutrosophic valued (and generalized or G) metric spaces for the first time. Besides, we newly determine a mathematical model for clustering the neutrosophic big data sets using G-metric. Furthermore, relative weighted neutrosophic-valued distance and weighted cohesion measure, is defined for neutrosophic big data set. We offer a very practical method for data analysis of neutrosophic big data although neutrosophic data type (neutrosophic big data) are in massive and detailed form when compared with other data types.

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42

Suryoto, Suryoto, Harjito Harjito, and Titi Udjiani. "MODUL NEUTROSOFIK KUAT." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 2 (November 30, 2018): 100. http://dx.doi.org/10.14710/jfma.v1i2.15.

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Given any neutrosophic ring with unity and a commutatively additive neutrosophic group. Then we can formed a neutrosophic algebraic structure is called a strong neutrosphic module. From the concept of weak neutrosophic module we extend to the concept of strong neutrosophic module. In this paper, also elementary properties of strong neutrosophic module are given.

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43

Muhiuddin, G. "p-ideals of BCI-algebras based on neutrosophic N -structures." Journal of Intelligent & Fuzzy Systems 40, no. 1 (January 4, 2021): 1097–105. http://dx.doi.org/10.3233/jifs-201309.

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In this paper, neutrosophic N -structures are applied to p-ideals of BCI-algebras. In fact, we introduce the notion of neutrosophic N -p-ideal in BCI-algebras, and investigate several properties. Further, we present characterizations of neutrosophic N -p-ideal. Moreover, we consider relations between a neutrosophic N -ideal and a neutrosophic N -p-ideal. Also, we provide conditions for a neutrosophic N -ideal to be a neutrosophic N -p-ideal. Furthermore, it is proved that the neutrosophic N -structure Q N G over Q is a neutrosophic N p -ideal of Q ⇔ G is a p-ideal of Q where G is a non-empty subset of a BCI-algebras Q.

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44

Jin, Qiu, Kai Hu, Chunxin Bo, and Lingqiang Li. "A New Single-Valued Neutrosophic Rough Sets and Related Topology." Journal of Mathematics 2021 (July 17, 2021): 1–14. http://dx.doi.org/10.1155/2021/5522021.

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(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

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45

Narmada Devi, R., N. Kalaivani, S. Broumi, and K. A.Venkatesan. "Characterizations of Strong and Balanced Neutrosophic Complex Graphs." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 593. http://dx.doi.org/10.14419/ijet.v7i4.10.21290.

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In this paper, the concepts of neutrosophic complex graph, complete neutrosophic complex graph, strong neutrosophic complex graph, balanced neutrosophic complex graph and strictly balanced neutrosophic complex graph are introduced. Some of the interesting properties and related examples are established.

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46

Huang, Liangsong, Yu Hu, Yuxia Li, P. K. Kishore Kumar, Dipak Koley, and Arindam Dey. "A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications." Mathematics 7, no. 6 (June 17, 2019): 551. http://dx.doi.org/10.3390/math7060551.

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Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the μ -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here.

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47

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. On one hand, we define generalized interval neutrosophic lower and upper approximation operators through constructive approach. Moreover, we investigate the relevance between generalized interval neutrosophic lower (upper) approximation operators and particular interval neutrosophic relations. On the other hand, we study axiomatic characterizations of generalized interval neutrosophic approximation operators, and also show that different axiom sets of theoretical interval neutrosophic operators make sure the existence of different classes of INRs that yield the same interval neutrosophic approximation operators. Finally, we introduce generalized interval neutrosophic rough sets on two universes and a universal algorithm of multi-attribute decision making based on generalized interval neutrosophic rough sets on two universes. Besides, an example is given to demonstrate the validity of the new rough set model.

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48

Şahin, Mehmet, and Abdullah Kargın. "Neutrosophic triplet normed space." Open Physics 15, no. 1 (November 10, 2017): 697–704. http://dx.doi.org/10.1515/phys-2017-0082.

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AbstractIn this paper; new properties for neutrosophic triplet groups are introduced. A notion of neutrosophic triplet metric space is given and properties of neutrosophic triplet metric spaces are studied. Neutrosophic triplet vector space and neutrosophic triplet normed space are also studied and some of their properties are given. Furthermore, we also show that these neutrosophic triplet notionsare different from the classical notions.

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49

Khan, Vakeel A., Ayhan Esi, Mobeen Ahmad, and Mohammad Daud Khan. "Continuous and bounded linear operators in neutrosophic normed spaces." Journal of Intelligent & Fuzzy Systems 40, no. 6 (June 21, 2021): 11063–70. http://dx.doi.org/10.3233/jifs-202189.

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In this article, we show that the addition and scalar multiplication in neutrosophic normed spaces are continuous. The neutrosophic boundedness and continuity of linear operators between neutrosophic normed spaces are examined. Moreover, we analyzed that the set of all neutrosophic continuous linear operators and the set of all neutrosophic bounded linear operators from neutrosophic normed spaces into another are vector spaces.

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Jun, Young Bae, Seok-Zun Song, and Seon Jeong Kim. "Neutrosophic Quadruple BCI-Positive Implicative Ideals." Mathematics 7, no. 5 (April 28, 2019): 385. http://dx.doi.org/10.3390/math7050385.

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By considering an entry (i.e., a number, an idea, an object, etc.) which is represented by a known part ( a ) and an unknown part ( b T , c I , d F ) where T , I , F have their usual neutrosophic logic meanings and a , b , c , d are real or complex numbers, Smarandache introduced the concept of neutrosophic quadruple numbers. Using the concept of neutrosophic quadruple numbers based on a set, Jun et al. constructed neutrosophic quadruple BCK/BCI-algebras and implicative neutrosophic quadruple BCK-algebras. The notion of a neutrosophic quadruple BCI-positive implicative ideal is introduced, and several properties are dealt with in this article. We establish the relationship between neutrosophic quadruple ideal and neutrosophic quadruple BCI-positive implicative ideal. Given nonempty subsets I and J of a BCI-algebra, conditions for the neutrosophic quadruple ( I , J ) -set to be a neutrosophic quadruple BCI-positive implicative ideal are provided.

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