Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)

Florentin

doi:https://doi.org/10.54216/PAMDA.030103

Full Length Article

Volume 3 • Issue 1 • PP: 29-48 • 2023

Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)

Florentin Smarandache ^1*

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¹Emeritus Professor University of New Mexico Mathematics, Physics, and Natural Science Division 705 Gurley Ave., Gallup, NM 87301, USA

* Corresponding Author.

DOI https://doi.org/10.54216/PAMDA.030103

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Received: May 17, 2023 Revised: August 13, 2023 Accepted December 22, 2023

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Abstract

We introduce for the first time the appurtenance equation and inclusion equation, which help in understanding the operations with neutrosophic numbers within the frame of neutrosophic statistics. The way of solving them resembles the equations whose coefficients are sets (not single numbers).

Keywords

Real Neutrosophic Numbers Neutrosophic Statistics True Value True Set-Value Appurtenance Relationship Appurtenance Equation Inclusion Relationship Inclusion Equation Equality Equation with Set-Coefficients NonAppurtenance Equation NonInclusion Equation NonEquality Equation Operations with Neutrosophic Numbers

References

[1] F. Smarandache, Neutrosophic Statistics vs. Interval Statistics, and Plithogenic Statistics as the most general form of statistics (second edition), International Journal of Neutrosophic Science (IJNS), Vol. 19, No. 01, PP. 148-165, 2022, http://fs.unm.edu/NS/NeutrosophicStatistics-vs-IntervalStatistics.pdf

[2] Muhammad Aslam, A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method. Symmetry 2019, 11, 114, DOI: 10.3390/sym11010114, https://fs.unm.edu/NS/AVariableAcceptanceSampling.pdf

[3] Florentin Smarandache, Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics, Neutrosophic Systems with Applications, Vol. 15, 16-32, 2024.

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Smarandache, Florentin. "Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)." Prospects for Applied Mathematics and Data Analysis, vol. Volume 3, no. Issue 1, 2023, pp. 29-48. DOI: https://doi.org/10.54216/PAMDA.030103

Smarandache, F. (2023). Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised). Prospects for Applied Mathematics and Data Analysis, Volume 3(Issue 1), 29-48. DOI: https://doi.org/10.54216/PAMDA.030103

Smarandache, Florentin. "Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)." Prospects for Applied Mathematics and Data Analysis Volume 3, no. Issue 1 (2023): 29-48. DOI: https://doi.org/10.54216/PAMDA.030103

Smarandache, F. (2023) 'Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)', Prospects for Applied Mathematics and Data Analysis, Volume 3(Issue 1), pp. 29-48. DOI: https://doi.org/10.54216/PAMDA.030103

Smarandache F. Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised). Prospects for Applied Mathematics and Data Analysis. 2023;Volume 3(Issue 1):29-48. DOI: https://doi.org/10.54216/PAMDA.030103

F. Smarandache, "Foundation of Appurtenance and Inclusion Equations for Constructing the Operations of Neutrosophic Numbers Needed in Neutrosophic Statistics (revised)," Prospects for Applied Mathematics and Data Analysis, vol. Volume 3, no. Issue 1, pp. 29-48, 2023. DOI: https://doi.org/10.54216/PAMDA.030103

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