Volume 6 , Issue 2 , PP: 23-37, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Prem Kumar Singh 1 *
Doi: https://doi.org/10.54216/JNFS.060203
Recently, several researchers paid attention towards dealing the data sets beyond Non-Euclidean geometry. To achieve this goal, Turiyam set and its properties is introduced for precise measurement of uncertainty in data sets beyond acceptation, rejection and uncertain parts. However the characterization of uncertainty requires a new operator and method. To resolve this issue, the current paper introduces a method for precise characterization of fourth dimensional data based on Turiyam operator and its complement with an illustrative example. The proposed method also compared the given method with Euclidean, Non-Euclidean, and NeutroGeometry data characterization.
Fourth Dimensions , Knowledge representation , Non-Euclidean , Quaternion , Unknown , Turiyam set
[1] Srinivasan N (2020) “Consciousness without content: A look at evidence and prospects”. Front. Psychology, 11:1992, https://doi.org/10.3389/fpsyg.2020.01992
[2] Ippoliti E (2019) “Heuristics and Inferential Microstructures: The Path to Quaternions”. Foundations of Science, 24: 411–425
[3] Atangana A, and Mekkaoui T (2019) “Trinition the complex number with two imaginary parts: Fractal, chaos and fractional calculus”. Chaos Solitons and Fractals, 128: 366-381
[4] Singh. P.K. (2021) “Turiyam set a fourth dimension data representation”. Journal of Applied Mathematics and Physics, 9(7): 1821-1828, doi: 10.4236/jamp.2021.97116
[5] Singh. P.K. (2021) “Fourth dimension data representation and its analysis using Turiyam Context”. Journal of Computer and Communications, 9(6): 222-229, doi: 10.4236/jcc.2021.96014
[6] Singh. P.K.(2021) “Data with Turiyam set for fourth dimension quantum information processing”. Journal of Neutrosophic and Fuzzy Systems, 1(1):9-23, doi: https://doi.org/10.54216/JNFS.010101
[7] Birkhoff G.D. (1932) “A Set of Postulates for Plane Geometry (Based on Scale and Protractors)”. Annals of Mathematics, 33.
[8] Lobachevsky N. (2010) “Pangeometry, Translator and Editor: A. Papadopoulos”. Heritage of European Mathematics Series. European Mathematical Society, 4.
[9] Bhattacharya S.(2004) “A model to a Smarandache Geometry”. http://fs.unm.edu/ModelToSmarandacheGeometry.pdf
[10] Smarandache F. (2021) “NeutroGeometry & AntiGeometry are alternatives and generalizations of the Non-Euclidean Geometries”. Neutrosophic Sets and Systems, 46:456-476, http://fs.unm.edu/NSS/NeutroGeometryAntiGeometry31.pdf
[11] Smarandache F. (2020) “NeutroAlgebra is a Generalization of Partial Algebra”. International Journal of Neutrosophic Science, 2: 8-17, 2020. doi: http://doi.org/10.5281/zenodo.3989285
[12] Singh P.K.(2021) “Anti-geometry and NeutroGeometry Characterization of Non-Euclidean Data”. Journal of Neutrosophic and Fuzzy Systems, 1(1):24-33, doi: https://doi.org/10.54216/JNFS.0101012
[13] Singh P.K. (2022) “NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns”. In: Theory and Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, Chapter 6, doi: 10.4018/978-1-6684-3495-6,
[14] Singh P.K. (2022) “Data with Non-Euclidean Geometry and its Characterization”. Journal of Artificial Intelligence and Technology, 2(1): 3-8, doi: 10.37965/jait.2021.12001
[15] Deng X., and Papadimitriou C. H. (1990) “Exploring an unknown graph". In: Proceedings of 31st Annual Symposium on Foundations of Computer Science, 1:355-361, doi: 10.1109/FSCS.1990.89554.
[16] Lawrence S. (2015) “Life, architecture, mathematics and fourth dimensions”. Nexus Network Journal, 17: 587-604
[17] Pandey LK, Ojha K. K., Singh P. K., Singh C. K., Dwivedi S., Bergey E. A. (2016) “Diatoms image database of India (DIDI): a research tool”. Environmental Technology & Innovation, 5: 148-160. https://doi.org/10.1016/j.eti.2017.02.005
[18] Fábri, C. and Császár, A. G. (2018) “Vibrational quantum graphs and their application to the quantum dynamics of CH5+”. Phys. Chem. Chem. Phys., 20:16913-16917, doi: https://doi.org/10.1039/C8CP03019G
[19] Irmak E., and Kurtuldu, Ö. (2015) “Concept of 4th Dimension for Databases”. In: Proceedings of 2015 IEEE 14th International Conference on Machine Learning and Applications (ICMLA), pp. 1159-1162, doi: 10.1109/ICMLA.2015.186.
[20] Bal M., Singh P. K., Ahmad K. D. (2022) “An Introduction To The Symbolic Turiyam R-Modules and Turiyam Modulo Integers”. Journal of Neutrosophic and Fuzzy Systems, 2(2): 8-19, doi: https://doi.org/10.54216/JNFS.020201
[21] Singh P.K., Ahmad K. D., Bal M., Aswad M. (2022) “On The Symbolic Turiyam Rings”. Journal of Neutrosophic and Fuzzy Systems, 1(2):80-88, doi : https://doi.org/10.54216/JNFS.010204
[22] Bal M., Singh P. K., Ahmad K. D. (2022) “A Short Introduction To The Concept Of Symbolic Turiyam Matrix”. Journal of Neutrosophic and Fuzzy Systems, 2 (1): 88-99, doi : https://doi.org/10.54216/JNFS.020108
[23] Bal M., Singh P. K., Ahmad K. D. (2022) “A Short Introduction To The Symbolic Turiyam Vector Spaces and Complex Numbers”. Journal of Neutrosophic and Fuzzy Systems, 2(1): 76-87, doi : https://doi.org/10.54216/JNFS.020107
[24] Jafari, S., Sprott, J.C. & Golpayegani, S.M.R.H. (2016) “Layla and Majnun: a complex love story”. Nonlinear Dyn 83, 615–622, https://doi.org/10.1007/s11071-015-2351-3
[25] Singh P. K. (2022) “t-index: Entropy based random document and citation analysis using average h-index”. Scientrometrics, 127:637-660, doi: 10.1007/s11192-021-04222-4
[26] Singh P.K. (2022) “Data with Rough Attributes and its Reduct Analysis”. Journal of Neutrosophic and Fuzzy Systems, 2(1):31-39, doi: https://doi.org/10.54216/JNFS.020104
[27] Belnap J. N. (1975) “A useful four-valued logic”. In J. Michael Dunn and George Epstein, editors, Proceedings of the Fifth International Symposium on Multiple-Valued Logic, Modern Uses of Multiple-Valued Logic. Indiana University, D. Reidel Publishing Company, pp 8-37.
[28] Font JM (1997) “Belnap's Four-Valued Logic and De Morgan Lattices”. In: Logic Journal of the IGPL, 5(3):1-29, doi: 10.1093/jigpal/5.3.1-e.
[29] Granados C. (2022) “A note on AntiGeometry and NeutroGeometry and their application to real life”. Neutrosophic Sets and Systems, 49:579-593. DOI: 10.5281/zenodo.6466520
[30] Singh P. K. (2022) “Non-Euclidean, Anti-Geometry and NeutroGeometry Characterization”. International Journal of Neutrosophic Sciences, 18(3): 8-19, doi : https://doi.org/10.54216/IJNS.180301
[31] Singh P.K. (2022) “Quaternion Set for Dealing Fluctuation in Quantum Turiyam Cognition”. Journal of Neutrosophic and Fuzzy Systems, Vol 4, Issue 2, pp. 57-64, doi: https://doi.org/10.54216/JNFS.040205
[32] Singh, P. K. (2022) “Four-Way Turiyam set-based human quantum cognition analysis”. Journal of Artificial Intelligence and Technology, 2(4), 144-151
[33] Ani A., Mashadi M., Sri G. (2023) "Invers Moore-Penrose pada Matriks Turiyam Simbolik Real." Jambura Journal of Mathematics 5, no. 1, pp. 95-114.
[34] Smarandache F. (2023) “Introduction to the symbolic plithogenic algebraic structures (revisited)”. Neutrosophic Set and System, 53, 653–665, 2023.
[35] Singh Pritpal (2023) “Ambiguous Set Theory: A New Approach to Deal with Unconsciousness and Ambiguousness of Human Perception”. Journal of Neutrosophic and Fuzzy Systems, Vol. 5 , No. 1 , pp. 52-58, 2023
[36] Silva, M., “The Latest Advances on AI and Robotics Applications”. Journal of Artificial Intelligence and Technology, Vol. 2, Issue 4, pp.131-131, 2022.
[37] S. Broumi, M. Lathamaheswari, Singh P. K., A. A. Ouallane, A. Bakhouyi, A. Bakali, M. Talea, A. Dhital, N. Deivanayagampillai (2022) “An Intelligent Traffic Control System Using Neutrosophic Sets, Rough sets, Graph Theory, Fuzzy sets and its Extended Approach: A Literature Review”. Neutrosophic Sets and Systems, Vol. 50, pp. 11-46, 2022.
[38] Singh P. K. (2023) “Four-Way Turiyam based Characterization of Non-Euclidean Geometry. Journal of Neutrosophic and Fuzzy Systems, Vol. 5 , No. 2 , pp. 69-80, doi : https://doi.org/10.54216/JNFS.050207
[39] Panaite, P., & Pelc, A. (1999) “Exploring unknown undirected graphs”. Journal of Algorithms, Vol. 33, Issue 2, pp. 281-295.
[40] Ganati, G.A., Repalle V.N.S.R., & Ahebo, M.A. (2023) “Relations in Context of Turiyam set”. BMC Research Notes, Vol. 16, Issue 49, https://doi.org/10.1186/s13104-023-06292-4
[41] Ganati, G.A., Repalle V.N.S.R., Ahebo, M.A., M Amini (2023) “Turiyam Graphs and its Applications”, Information Sciences Letters, Vol. 12, No. 6, pp. 2423-2434
[21] Singh P.K., Ahmad K. D., Bal M., Aswad M. (2022) “On The Symbolic Turiyam Rings”. Journal of Neutrosophic and Fuzzy Systems, 1(2):80-88, doi : https://doi.org/10.54216/JNFS.010204
