Volume 18 • Issue 3 • PP: 157-165 • 2022
Neutrosophical dynamic programming
View PDF Abstract
The great development that science has witnessed in all fields has reduced the risks and losses resulting from undertaking any business or projects. Since the emergence of the science of operations research, many life issues have been addressed by relying on it, and by using its methods, we have been able to establish projects and businesses and use the available capabilities in an ideal manner. Which achieved great success in all areas and reduced the losses of all kinds, whether material or human, that we were exposed to because of carrying out these works or projects without prior study. We are now able to model, analyze and solve a wide range of problems that can be broken down into a set of partial problems using dynamic programming. Programming that is used to find the optimal solution in a multi-step situation that involves a set of related decisions. In this research, we study one of the operations research problems that are solved using dynamic programming. It is the problem of creating an expressway between two cities, using the neutrosophic logic. The logic that takes into account all the specific and non-specific data and takes into account all the circumstances that can face us during the implementation of the project. The goal of studying this issue is to determine the optimal total cost, which is related to the partial costs presented by the study prepared for this project. In order to avoid losses we will take the partial costs neutrosophic values of the form , where represents the minimum partial cost in stage and represents the upper limit of the partial cost in stage . Through the indeterminacy offered by neutrosophic logic, we are able to find the ideal solution that will bring us the lowest possible cost for constructing this expressway. It takes into account all the circumstances that may encounter us in our study, and we will present an applied example that illustrates the study.
Keywords
References
1. Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set,
Neutrosophic Probability. American Research Press, Rehoboth, NM, 1999.
2. Smarandache, F. Introduction to Neutrosophic statistics, Sitech & Education Publishing, 2014.
3. Smarandache, F, Neutrosophic set a generalization of the intuitionistic fuzzy sets. Inter. J. Pure Appl.
Math., 24, 287 – 297, 2005.
4. Salama, A. A, Smarandache, F, and Kroumov, V, Neutrosophic crisp Sets & Neutrosophic crisp
Topological Spaces. Sets and Systems, 2(1), 25-30, 2014
5. A.A. Salama- F. Smarandache- Neutrosophic crisp set Theory Educational- Education Publishing 1313
Chesapeake, Avenue, Columbus, Ohio 43212- 2015.
6. Salama, A. A and F. Smarandache. "Neutrosophic crisp probability theory & decision making process."
Critical Review: A Publication of Society for Mathematics of Uncertainty, vol. 12, p. 34-48, 2016.
7. Alhabib .R, M. Ranna, H. Farah and A. A Salama, ''Foundation of Neutrosophic Crisp Probability Theory'',
Neutrosophic Operational Research, Volume III , Edited by Florentin Smarandache, Mohamed Abdel-
Basset and Dr. Victor Chang (Editors), pp.49-60, 2017
8. Alhabib .R, M. Ranna, H. Farah and A. A Salama.(2018). Some neutrosophic probability distributions.
Neutrosophic Sets and Systems, 22, 30-38, 2018.
9. Aslam, M., Khan, N. and AL-Marshadi, A. H. (2019). Design of Variable Sampling Plan for Pareto
Distribution Using Neutrosophic Statistical Interval Method, Symmetry, 11 (1), 80.
10. Alhabib .R, A. A Salama, "Using Moving Averages To Pave The Neutrosophic Time Series'',
International Journal of Neutrosophic Science (IJNS), Volume III, Issue 1, PP: 14-20, 2020.
11. Smarandache .F, Introduction to Neutrosophic Measure Neutrosophic Integral and Neutrosophic
Probability, 2015. http://fs.gallup. unm.edu/ eBooks-otherformats.htm.
12. Jdid .M, Alhabib.R and Salama.A.A, Fundamentals of Neutrosophical Simulation for Generating Random
Numbers Associated with Uniform Probability Distribution, Neutrosophic Sets and Systems, 49, 2022
13. Jdid .M, Alhabib.R ,and Salama.A.A, The static model of inventory management without a deficit with
Neutrosophic logic, International Journal of Neutrosophic Science (IJNS), Volume 16, Issue 1, PP: 42-48,
2021.
14. Jdid .M, Alhabib.R ,Bahbouh .O , Salama.A.A and Khalid .H, The Neutrosophic Treatment for multiple
storage problem of finite materials and volumes, International Journal of Neutrosophic Science (IJNS),
Volume 18, Issue 1, PP: 42-56, 2022.
15. Jdid .M, Salama.A.A , Alhabib.R ,Khalid .H, and Alsuleiman .F, Neutrosophic Treatment of the static
model of inventory management with deficit , International Journal of Neutrosophic Science (IJNS),
Volume 18, Issue 1, PP: 20-29, 2022.
16. Jdid .M, Salama.A.A and Khalid .H, Neutrosophic handling of the simplex direct algorithm to define the
optimal solution in linear programming , International Journal of Neutrosophic Science (IJNS), Volume 18,
Issue 1, PP: 30-41, 2022.
17. Jdid .M, Alhabib.R ,Khalid .H, and Salama.A.A, the Neutrosophic Treatment of the static model for the
inventory management with safety reserve , International Journal of Neutrosophic Science (IJNS), Volume
18, Issue 2, PP: 262-271, 2022.
18. Jdid .M, and Khalid .H, mysterious Neutrosophic linear models , International Journal of Neutrosophic
Science (IJNS), Volume 18, Issue 2, PP: 243-253, 2022.
19. Hamd. Ibtisam - Analysis of engineering systems. Tishreen University Publications.1998.
20. Bukajh J.S - . Mualla, W... and others - Operations Research Book translated into Arabic - The Arab Center
for Arabization, Translation, Authoring and Publishing -Damascus -1998. . (Arabic version).
21. Al Hamid .M , Mathematical programming , Aleppo University , Syria , 2010. (Arabic version).
22. E. Khalid, H and Ahmed K. E. "The Duality Approach of the Neutrosophic Linear
Programming." Neutrosophic Sets and Systems 46, 1 (2021).
Cite This Article
Choose your preferred format