133 71
Full Length Article
International Journal of Neutrosophic Science
Volume 18 , Issue 3, PP: 21-29 , 2022 | Cite this article as | XML | Html |PDF


Non-Euclidean, AntiGeometry, and NeutroGeometry Characterization

Authors Names :   Prem Kumar Singh   1 *  

1  Affiliation :  Department of Computer Science and Engineering, Gandhi Institute of Technology and Management-Visakhapatnam, Andhra Pradesh 530045, India

    Email :  premsingh.csjm@gmail.com , premsingh.csjm@yahoo.com

Doi   :   https://doi.org/10.54216/IJNS.180301

Received:January 09, 2022 Accepted: April 03, 2022

Abstract :

Recently, a problem is addressed about dealing the difference among Non-Euclidean, AntiGeometry and NeutroGeoemtry data sets. The problem arises while partial negation of Euclidean Geometry, full negation of Euclidean or Hybrid mode. In case of undefined geometry also many researchers raised the questions. To tackle this issue, the current paper provides some examples for Non-Euclidean, AntiGeometry, and Neutrogemoetry for better understanding. 

Keywords :

AntiGeometry; Euclidean geometry; Graph Analytics; Knowledge representation; NeutroGeometry , Non-Euclidean geometry; Turiyam; Unknown graph.

References :

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

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

[3]     Singh P. K., “AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets, Journal of Neutrosophic and Fuzzy Systems, Nov 2021, Volume 1, Issue 1, pp. 24-33, DOI: https://doi.org/10.54216/JNFS.0101012   

[4]     Singh PK, “Data with Non-Euclidean Geometry and its Characterization”, Journal of Artificial Intelligence and Technology, Jan 2022, Volume 2, Issue 1, pp. 3-8 , DOI: 10.37965/jait.2021.12001 

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

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

[7]     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

[8]     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

[9]     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

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

[11]   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

[12]   Singh P. K., “NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns”. NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, April 2022, Chapter 6,  DOI: 10.4018/978-1-6684-3495-6

[13]   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.

[14]   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

[15]   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

[16]   Bal M, Singh PK, Ahmad KD, A Short Introduction To The Symbolic Turiyam Vector Spaces and Complex Numbers, Journal of Neutrosophic and Fuzzy Systems, Vol. 2 , No. 1 , pp. 76-87 , 2022, (Doi   :  https://doi.org/10.54216/JNFS.020107)

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

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

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

[20]   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

[21]   Singh PK, “Data with Rough Attributes and its Reduct Analysis, Journal of Neutrosophic and Fuzzy Systems, Vol 2, Issue 1, pp. 31-39, Mar 2022, DOI: https://doi.org/10.54216/JNFS.020104

[22]   Deng X, and Papadimitriou CH, "Exploring an unknown graph," In: Proceedings of 31st Annual Symposium on Foundations of Computer Science, Vol. 1, pp. 355-361, 1990, doi: 10.1109/FSCS.1990.89554.

[23]   Fábri, C. and  Császár, A. G., “Vibrational quantum graphs and their application to the quantum dynamics of CH5+”, Phys. Chem. Chem. Phys., Vol. 20, pp. 16913-16917, 2018, doi: https://doi.org/10.1039/C8CP03019G

[24]   Singh, P,K, “Complex Plithogenic Set”, International Journal of Neutrosophic Sciences, Vol 18, Issue 1, pp. 57-72, 2022, doi : https://doi.org/10.54216/IJNS.180106

[25]   Dillon, M.I. “Neutral Geometry”. In: Geometry Through History. Springer, Cham. 2018, https://doi.org/10.1007/978-3-319-74135-2_2


Cite this Article as :
Prem Kumar Singh, Non-Euclidean, AntiGeometry, and NeutroGeometry Characterization, International Journal of Neutrosophic Science, Vol. 18 , No. 3 , (2022) : 21-29 (Doi   :  https://doi.org/10.54216/IJNS.180301)