1
Faculty of Science, Damascus University, Damascus, Syria
(maissam.jdid66@damascusuniversity.edu.sy)
2
University of New Mexic Mathematics, Physics and Natural Sciences Division 705 Gurley Ave., Gallup, NM 87301, USA
(smarand@unm.edu)
Abstract :
The focus of operations research is the existence of a problem that requires making an appropriate decision that helps reduce risk and achieves a good level of performance. Operations research methods depend on formulating realistic issues through mathematical models consisting of a goal function and constraints, and the optimal solution is the ideal decision, despite the multiplicity of these methods. However, we encounter many complex issues that cannot be represented mathematically, or many issues that cannot be studied directly. Here comes the importance of the simulation process in all branches of science, as it depends on applying the study to systems similar to real systems and then projecting this. The results if they fit on the real system. So simulation is the process of building, testing, and running models that simulate complex phenomena or systems using specific mathematical models. The simulation process depends on generating a series of random numbers subject to a regular probability distribution in the field [0, 1], and then converting these random numbers into random variables subject to the distribution law. Probability, according to which the system to be simulated operates, using appropriate techniques for both the probability density function and the cumulative distribution function. Classical studies have provided many techniques that are used during the simulation process, and to keep pace with the great scientific development witnessed by our contemporary world, we found that a new vision must be presented for this. Techniques A vision based on the concepts of neutrosophics, the science founded by the American mathematical philosopher Florentin Smarandache. The year 1995, in which new concepts of probabilities and probability distributions are used, as we presented in previous research some techniques from a neutrosophic perspective, and as an extension of what we presented previously, we present in this research a neutrosophic vision of the Box and Muller technique used to generate random variables that follow a normal distribution.
Keywords :
Simulation; Neutrosophic simulation; Neutrosophic normal distribution; Generation of neutrosophic random variables that follow the normal distribution; Box and Muller technique
References :
[1] Florentin Smarandache, Maissam Jdid, On Overview of Neutrosophic and Plithogenic Theories and Applications, Doi :https://doi.org/10.54216/PAMDA.020102
[2] G. Dhanalakshmi, S. Sandhiya, Florentin Smarandache, Selection of the best process for desalination under a Treesoft set environment using the multi-criteria decision-making method,
Doi:https://doi.org/10.54216/IJNS.230312, Vol,23, No,3
[3] Mountajab Alhasan, Malath F Alaswad. A Study of the Movement of a Neutrosophic Material Point in the Neutrosophic Plane by Using a Neutrosophic AH-Isometry, Journal Prospects for Applied Mathematics and Data Analysis, Doi :https://doi.org/10.54216/PAMDA.020101,Vol 2, No 1, 2023.
[4] Maissam Jdid, Florentin Smarandache, Graphical Method for Solving Neutrosophical Nonlinear Programming Models, International Journal of Data Science and Big Data Analytics, Vol,3, No,2
[5] Mona Gharib, Florentin Smarandache, Mona Mohamed, CSsEv: Modelling QoS Metrics in Tree Soft Toward Cloud Services Evaluator based on Uncertainty Environment, Doi :https://doi.org/10.54216/IJNS.230204, Vol,23, No,2
[6] Fatma Taher, Neutrosophic Multi-Criteria Decision-Making Methodology to Identify Key Barriers in Education, https://doi.org/10.54216/IJNS.220410
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[8] Marwah Yahya Mustafa , Zakariya Yahya Algamal, Neutrosophic inverse power Lindley distribution: A modeling and application for bladder cancer patients, Doi :https://doi.org/10.54216/IJNS.210218
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[15] Maissam Jdid, A. Salama, Using the Inverse Transformation Method to Generate Random Variables that follow the Neutrosophic Uniform Probability Distribution, Doi :https://doi.org/10.54216/JNFS.060202
[16] Maissam Jdid, Rafif Alhabib and A. A. Salama, The Basics of Neutrosophic Simulation for Converting Random Numbers Associated with a Uniform Probability Distribution into Random Variables Follow an Exponential Distribution, Neutrosophic Sets and Systems, Vol. 53, 2023, pp. 358-366. DOI: 10.5281/zenodo.7536049
[17] Maissam Jdid, Said Broumi, Neutrosophical Rejection and Acceptance Method for the Generation of Random Variables, Neutrosophic Sets and Systems, Vol. 56, 2023, pp. 153-166. DOI: 10.5281/zenodo.8194749
[18] Maissam Jdid and Nada A. Nabeeh, Generating Random Variables that follow the Beta Distribution Using the Neutrosophic Acceptance-Rejection Method, Neutrosophic Sets and Systems, Vol. 58, 2023, pp. 139-148. DOI: 10.5281/zenodo.8404445
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| Style | # |
|---|---|
| MLA | Maissam Jdid, Florentin Smarandache. "The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution." International Journal of Neutrosophic Science, Vol. 23, No. 4, 2024 ,PP. 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |
| APA | Maissam Jdid, Florentin Smarandache. (2024). The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |
| Chicago | Maissam Jdid, Florentin Smarandache. "The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution." Journal of International Journal of Neutrosophic Science, 23 no. 4 (2024): 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |
| Harvard | Maissam Jdid, Florentin Smarandache. (2024). The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution. Journal of International Journal of Neutrosophic Science, 23 ( 4 ), 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |
| Vancouver | Maissam Jdid, Florentin Smarandache. The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 4 ): 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |
| IEEE | Maissam Jdid, Florentin Smarandache, The Box and Muller Technique for Generating Neutrosophic Random Variables Follow a Normal Distribution, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 4 , (2024) : 83-87 (Doi : https://doi.org/10.54216/IJNS.230406) |