808 769
Full Length Article
Journal of Neutrosophic and Fuzzy Systems
Volume 1 , Issue 1, PP: 24-33 , 2021 | Cite this article as | XML | Html |PDF

Title

Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data

  Prem Kumar Singh 1 *

1  Department of Computer Science and Engineering, Gandhi Institute of Technology and Management-Visakhapatnam, Andhra Pradesh 530045, India
    (premsingh.csjm@gmail.com , premsingh.csjm@yahoo.com (ORCID: 0000-0003-1465-6572))


Doi   :   https://doi.org/10.54216/JNFS.010102


Abstract :

Recently, a problem is addressed while dealing with fourth dimensional or non-Euclidean data sets. These are the data sets does not follow one of the postulates established by Euclid specially the parallel postulates. In this case, the precise representation of these data sets is major issues for knowledge processing tasks. Hence, the current paper tried to introduce some non-Euclidean geometry or Anti-Geometry methods and its examples for various applications. 

Keywords :

Antigeometry; Euclidean geometry; Graph Analytics; Knowledge representation; Multi-attributes; NeutroGeometry , Non-Euclidean geometry

References :

[1]      Singh P.K., “Turiyam set a fourth dimension data representation. Journal of Applied Mathematics and Physics, Vol. 9, Issue 7, pp. 1821-1828, 2021, DOI: 10.4236/jamp.2021.97116

[1]         Singh P.K., “Fourth dimension data representation and its analysis using Turiyam Context”. Journal of Computer and Communications, Vol. 9, Issue 6, pp. 222-229, 2021 doi: 10.4236/jcc.2021.96014

[2]         Birkhoff G.D., “A Set of Postulates for Plane Geometry (Based on Scale and Protractors)”. Annals of Mathematics, Vol. 33, 1932.

[3]          Lobachevsky N., “Pangeometry, Translator and Editor: A. Papadopoulos. Heritage of European Mathematics Series". European Mathematical Society, Vol. 4, 2010.

[4]         Bhattacharya S., “A model to a Smarandache Geometry”. 2004, http://fs.unm.edu/ModelToSmarandacheGeometry.pdf

[5]         Popov, M. R., “The Smarandache Non-Geometry. Abstracts of Papers Presented to the  American Mathematical Society Meetings, Vol. 17, Issue 3, pp. 595, 1996.

[6]         Kuciuk L., Antholy M., “An introduction to the Smarandache geometries. JP Journal of Geometry & Topology”, Vol. 5, Issue 1, 77-81, 2005, http://fs.unm.edu/IntrodSmGeom.pdf

[7]         Smarandache F., “Introduction to NeutroAlgebraic Structures and AntiAlgebraic Structures”. In: Advances of Standard and Nonstandard Neutrosophic Theories, Pons Publishing House Brussels, Belgium, Vol. 6, pp. 240-265, 2019. http://fs.unm.edu/AdvancesOfStandardAndNonstandard.pdf

[8]         Smarandache F., “NeutroAlgebra is a Generalization of Partial Algebra”. International Journal of Neutrosophic Science, Vol. 2, pp. 8-17, 2020. DOI: http://doi.org/10.5281/zenodo.3989285

[9]         Al-Tahan M., Smarandache F., Davvaz B., “NeutroOrderedAlgebra: Applications to semigroups”. Neutrosophic Sets and System, Vol. 39, pp. 133–147, 2021.

[10]      Smarandache F., “NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries”. Neutrosophic Sets and Systems, Vol. 46, pp. 456-476, 2021. http://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf

[11]      Singh P. K., “NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns”. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, 2021, (Accepted for Publications)

[12]      Singh P. K., “ Data with Turiyam Set for Fourth Dimension Quantum Information Processing”.  Journal of Neutrosophic and Fuzzy Systems, Vol 1, Issue 1, pp. 9-23, 2021.

[13]      Singh P. K., “Air Quality Index Analysis Using Single-Valued Neutrosophic Plithogenic Graph for Multi-Decision Process”. International Journal of Neutrosophic Sciences, Vol 16, Issue 1, pp. 28-141, 2021. DOI: https://doi.org/10.54216/IJNS.160103

[14]      Russell B., “Introduction: An essay on the foundations of geometry”. Cambridge University Press, 1897. 

[15]       Coxeter H.S.M., “Non-Euclidean Geometry. University of Toronto Press, 1942. reissued 1998 by Mathematical Association of America.

[16]      James A. W., “Hyperbolic Geometry”. Second edition 2005, Springer.

[17]      Pandey L. K., Ojha K. K., Singh P.K., Singh C. S., Dwivedi S., Bergey E.A, “Diatoms image database of India (DIDI): a research tool”. Environmental Technology & Innovation, Vol. 5, pp. 148-160, 2016.  https://doi.org/10.1016/j.eti.2017.02.005

[18]      Kapoor P, Singh P. K., Ch. Aswani Kumar, “IT act Crime Pattern Analysis Using Regression and Correlation Matrix. In: Proceedings of 8thInternational Conference on Reliability, Infocom Technologies and Optimization 2020, pp. 1102-1106, 2020. doi: 10.1109/ICRITO48877.2020.9197835 

[19]      Tixeira da Silva J.A., Vuong Q.H., “The right to refuse unwanted citations: rethinking the culture of science around the citation”. Scientometrics, Vol. 126, pp. 5355–5360, 2021.

[21]    Subbotin A., Aref S.,  “Brain drain and brain gain in Russia: Analyzing international migration of researchers by discipline using Scopus bibliometric data 1996–2020”. Scientometrics, Vol. 126 pp. 7875–7900, 2021 https://doi.org/10.1007/s11192-021-04091-x

[22] Kosmulski M., “Posthumous co–authorship revisited”. Scientometrics, Vol. 126, pp. 8227– 8231, 2021

 


Cite this Article as :
Style #
MLA Prem Kumar Singh. "Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data." Journal of Neutrosophic and Fuzzy Systems, Vol. 1, No. 1, 2021 ,PP. 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)
APA Prem Kumar Singh. (2021). Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data. Journal of Journal of Neutrosophic and Fuzzy Systems, 1 ( 1 ), 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)
Chicago Prem Kumar Singh. "Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data." Journal of Journal of Neutrosophic and Fuzzy Systems, 1 no. 1 (2021): 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)
Harvard Prem Kumar Singh. (2021). Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data. Journal of Journal of Neutrosophic and Fuzzy Systems, 1 ( 1 ), 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)
Vancouver Prem Kumar Singh. Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data. Journal of Journal of Neutrosophic and Fuzzy Systems, (2021); 1 ( 1 ): 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)
IEEE Prem Kumar Singh, Anti-Geometry and NeutroGeometry Characterization of Non-Euclidean Data, Journal of Journal of Neutrosophic and Fuzzy Systems, Vol. 1 , No. 1 , (2021) : 24-33 (Doi   :  https://doi.org/10.54216/JNFS.010102)