Fuzzy Mathematics and Nonstandard Analysis Application to the Theory of Relativity

Transactions on Fuzzy Sets and Systems

مقاله 11، دوره 1، شماره 1، مرداد 2022، صفحه 143-154   

نوع مقاله: Original Article

شناسه دیجیتال (DOI): 10.30495/tfss.2022.1953823.1014

نویسندگان

John N Mordeson¹؛ Sunil Mathew^{* 2}

¹Department of Mathematics Creighton University Omaha, USA

²Department of Mathematics National Institute of Technology Calicut Calicut, India

چکیده

In this paper, we extend some results of nonstandard analysis to include concepts from fuzzy mathematics. Then we apply our results to issues from special and general relativity and the theory of light-clocks. The extension includes concepts of fuzzy numbers, continuity, and differentiability. Our goal is to provide a new research area in fuzzy mathematics.

کلیدواژه‌ها

Fuzzy logic؛ Nonstandard analysis؛ Theory of relativity

مراجع

[1] I. Davis, An Introduction to Nonstandard Analysis (2009). Available online: https://www.math.uchicago.edu.
[2] I. Goldberg, Lecture notes on nonstandard analysis (2014). Available online: https://www.math.uci.edu.
[3] R. A. Herrmann, Nonstandard Analysis Applied to Special and General Relativity-The Theory of Infinitesimal Light-Clocks (2014). Available online: https://arXiv:math/0312189v10 [math.GM].
[4] T. Imamura, Note on the definition of neutrosophic logic, Math. I. O. 7(2018). Available online: https://arXiv:1811.02961v1.
[5] E. Klement and R. Mesiar, L-fuzzy sets and ispmorphic lattices, are all the results really new? Mathematics, 6(146) (2018), 1-24.
[6] G. J. Klir and B. Yuan, Fuzzy Sets and Logic: Theory and Applications, Prentice Hall PTR, New Jersey, (1995).
[7] P. A. Loeb and M. Wolff, Nonstandard Analysis for the Working Mathematician, Kluwer Academic Publishers, USA, (2000).
[8] J. N. Mordeson and S. Mathew, Nonstandard fuzzy mathematics, Advances in Fuzzy Sets and Systems, 27 (2022), 35-52.
[9] J. N. Mordeson, S. Mathew and M. Binu, Applications of Mathematics of Uncertainty, Grand Challenges-Human Trafficking-Coronavirus-Biodiversity and Extinction, Springer Studies in Systems, Decision and Control, (2022).
[10] D. A. B. Rayo, Introduction to non-standard analysis. Available online: https://math.uchicago.edu REUPapers 2-15.
[11] A. Robinson, Nonstandard Analysis, North-Holland Publishing Co., (1966).
[12] E. Staunton, (R. Ryan Supervisor), Infinitesimals, nonstandard analysis and applications to finance, NUI Galway OE Gaillimh, National University of Ireland, Galway, (2013).