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Prospects for Applied Mathematics and Data Analysis
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Title

Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm

  Maissam Jdid 1 * ,   Florentin Smarandache 2

1  Faculty of Science, Damascus University, Damascus, Syria
    (maissam.jdid66@damascusuniversity.edu.sy)

2  University of New Mexico، Mathematics, Physics and Natural Sciences Division 705 Gurley Ave., Gallup, NM 87301, USA
    (smarand@unm.edu)

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Doi   :   https://doi.org/10.54216/PAMDA.020202

Received: March 12, 2023 Accepted: October 19, 2023

Abstract :

One of the most important theories in linear programming is the dualistic theory and its basic idea is that for every linear model has dual linear model, so that solving the original linear model gives a solution to the dual model. Therefore, when we solving the linear programming model, we actually obtain solutions for two linear models. In this research, we present a study of the models. The neutrosophic dual and the binary simplex algorithm, which works to find the optimal solution for the original and dual models at the same time. The importance of this algorithm is evident in that it is relied upon in several operations research topics, such as integer programming algorithms, some nonlinear programming algorithms, and sensitivity analysis in linear programming...

Keywords :

Neutrosophic Science; Neutrosophic Linear Models; Dual Models; Neutrosophic dual Linear Models; binary Simplex Algorithm.

References :

[1]    Florentin Smarandache, Maissam Jdid, On Overview of Neutrosophic and Plithogenic Theories and Applications, Applied Mathematics and Data Analysis, Vo .2, No .1, 2023

[2]    Maissam Jdid- Hla Hasan, The state of Risk and Optimum Decision According to Neutrosophic Rules, International Journal of Neutrosophic Science (IJNS), Vol. 20, No.1,2023

[3]    Mohammed Alshikho, Maissam Jdid, Said Broumi, Artificial Intelligence and Neutrosophic Machine learning in the Diagnosis and Detection of COVID 19, Journal Prospects for Applied Mathematics and Data Analysis, Vol 01, No,02 USA,2023

[4]    Maissam Jdid, Neutrosophic Nonlinear Models, Journal Prospects for Applied Mathematics and Data Analysis, Vo .2, No .1, 2023

[5]    Maissam Jdid, Neutrosophic Mathematical Model of Product Mixture Problem Using Binary Integer Mutant, Journal of Neutrosophic and Fuzzy Systems (JNFS), Vo .6, No .2, 2023

[6]    Maissam Jdid, The Use of Neutrosophic linear Programming Method in the Field of Education, Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education, Chapter 15, IGI-Global,2023

[7]    Maissam Jdid, Florentin Smarandache, Said Broumi, Inspection Assignment Form for Product Quality Control, Journal of Neutrosophic Systems with Applications, Vol. 1, 2023

[8]    Maissam Jdid, Said Broumi, Neutrosophic Rejection and Acceptance Method for the Generation of Random Variables, Neutrosophic Sets and Systems, NSS, Vol.56,2023

[9]    Maissam Jdid, Florentin Smarandache, The Use of Neutrosophic Methods of Operation Research in the Management of Corporate Work, Journal of Neutrosophic Systems with Applications, Vol. 3, 2023

[10] Maissam Jdid, Florentin Smarandache, Lagrange Multipliers and Neutrosophic Nonlinear Programming Problems Constrained by Equality Constraints Journal of Neutrosophic Systems with Applications, Vol. 6, 2023

[11] Maissam Jdid, Florentin Smarandache, Optimal Neutrosophic Assignment and the Hungarian Method, Journal Neutrosophic Sets and Systems, NSS Vol.57,2023

[12] Maissam Jdid, Florentin Smarandache, Graphical Method for Solving Neutrosophical Nonlinear Programming Models, Journal of Neutrosophic Systems with Applications, Vol. 9, 2023

[13] Maissam Jdid, Florentin Smarandache, Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Journal of Neutrosophic Systems with Applications, Vol. 10, 2023

[14] Maissam Jdid, Nada A Nabeeh Generating Random Variables that follow the Beta Distribution Using the Neutrosophic Acceptance-Rejection Method *1, Journal Neutrosophic Sets and Systems, NSS Vol.58,2023

[15] Maissam Jdid, Studying Transport Models with the Shortest Time According to the Neutrosophic Logic, Journal Neutrosophic Sets and Systems, NSS Vol.58,2023

[16] Florentin Smarandache, Maissam Jdid, NEUTROSOPHIC TRANSPORT AND ASSIGNMENT ISSUES, Publisher: Global Knowledge’s: 978_1 _59973_769_0

[17] Maissam Jdid, NEUTROSOPHIC TRANSPORT AND ASSIGNMENT ISSUES, Publisher: Global Knowledge’s: 978_1 _59973_770_6, (Arabic version).

[18] Maissam Jdid, AA Salama, Huda E Khalid ,Neutrosophic Handling of the Simplex Direct Algorithm to Define the Optimal Solution in Linear Programming ,International Journal of Neutrosophic Science, Vol.18,No. 1, 2022

[19] Maissam Jdid, Huda E Khalid, Mysterious Neutrosophic Linear Models, International Journal of Neutrosophic Science, Vol.18, No. 2, 2022

[20] Maissam Jdid, Florentin Smarandache, The Graphical Method for Finding the Optimal Solution for Neutrosophic linear Models and Taking Advantage of Non-Negativity Constraints to Find the Optimal Solution for Some Neutrosophic linear Models in Which the Number of Unknowns is More than Three, Journal Neutrosophic Sets and Systems, NSS Vol.58,2023

[21] Alali. Ibrahim Muhammad, Operations Research. Tishreen University Publications, 2004. (Arabic version).

[22] Al Hamid. Mohammed Dabbas, Mathematical programming, Aleppo University, Syria, 2010. (Arabic version).

[23] Linear and Nonlinear Programming-DavidG. Luenbrgrr.YinyuYe- Springer Science + Business Media-2015.

[24] Maissam Jdid, Bi-Linear Model of Natural Resource Use Published in Tver State University, 2002

[25] Maissam Jdid Operations Research, Faculty of Informatics Engineering, Al-Sham Private University Publications, 2021.

Cite this Article as :
Style #
MLA Maissam Jdid, Florentin Smarandache. "Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm." Prospects for Applied Mathematics and Data Analysis, Vol. 2, No. 2, 2023 ,PP. 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
APA Maissam Jdid, Florentin Smarandache. (2023). Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
Chicago Maissam Jdid, Florentin Smarandache. "Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm." Journal of Prospects for Applied Mathematics and Data Analysis, 2 no. 2 (2023): 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
Harvard Maissam Jdid, Florentin Smarandache. (2023). Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm. Journal of Prospects for Applied Mathematics and Data Analysis, 2 ( 2 ), 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
Vancouver Maissam Jdid, Florentin Smarandache. Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm. Journal of Prospects for Applied Mathematics and Data Analysis, (2023); 2 ( 2 ): 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
IEEE Maissam Jdid, Florentin Smarandache, Neutrosophic Treatment of Duality Linear Models and the Binary Simplex Algorithm, Journal of Prospects for Applied Mathematics and Data Analysis, Vol. 2 , No. 2 , (2023) : 08-21 (Doi   :  https://doi.org/10.54216/PAMDA.020202)
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