Study of the System of Uncertain Linear Differential Equations Under Neutrosophic Sense of Uncertainty
DOI:
https://doi.org/10.31181/sems31202536rKeywords:
System of differential equation, Uncertainty, Neutrosophic number, Neutrosophic equation, Neutrosophic derivativeAbstract
This paper considers a system of uncertain linear differential equations under the Neutrosophic uncertain environment. Suppose the mutual dependency of the dynamics of two variables is set on the mathematical manipulation under the scenario where the available information regarding initial states is imprecise and is given in the Neutrosophic sense of uncertainty. The concept of Neutrosophic differential equations can play a very effective role in this regard. The present chapter is engaged with a brief introduction of the theory of the system of Neutrosophic differential equations and the possible solution approaches. Combining different cases of Neutrosophic differentiability and the signs of the coefficients involved in the differential equations are taken for the synergetic study of the theory. At the end of the theory, a few physical phenomena are explored as possible applications of the proposed theory. For a better understanding and reliability of the proposed theory, numerical simulations and graphical visualizations are added to different pockets of this paper.
References
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Chang, S. S., & Zadeh, L. A. (1972). On fuzzy mapping and control. IEEE transactions on systems, man, and cybernetics, (1), 30-34. https://doi.org/10.1109/TSMC.1972.5408553
Dubois, D., & Prade, H. (1978). Operations on fuzzy numbers. International Journal of systems science, 9(6), 613-626. https://doi.org/10.1080/00207727808941724
Turksen, I. B. (1986). Interval valued fuzzy sets based on normal forms. Fuzzy sets and systems, 20(2), 191-210. https://doi.org/10.1016/0165-0114(86)90077-1
Atanassov, K. T., & Atanassov, K. T. (1999). Intuitionistic fuzzy sets (pp. 1-137). Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1870-3_1
Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis, 3, 1-105.
Pamucar, D., Yazdani, M., Obradovic, R., Kumar, A., & Torres‐Jiménez, M. (2020). A novel fuzzy hybrid neutrosophic decision‐making approach for the resilient supplier selection problem. International Journal of Intelligent Systems, 35(12), 1934-1986. https://doi.org/10.1002/int.22279
Pamucar, D., Deveci, M., Schitea, D., Erişkin, L., Iordache, M., & Iordache, I. (2020). Developing a novel fuzzy neutrosophic numbers based decision making analysis for prioritizing the energy storage technologies. International journal of hydrogen energy, 45(43), 23027-23047. https://doi.org/10.1016/j.ijhydene.2020.06.016
Das, S., Roy, B. K., Kar, M. B., Kar, S., & Pamučar, D. (2020). Neutrosophic fuzzy set and its application in decision making. Journal of Ambient Intelligence and Humanized Computing, 11, 5017-5029. https://doi.org/10.1007/S12652-020-01808-3
Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite study, 410-413.
Kumar, R., Edaltpanah, S. A., Jha, S., Broumi, S., & Dey, A. (2018). Neutrosophic shortest path problem. Infinite Study, 23, 5-15.
Chakraborty, A., Broumi, S., & Singh, P. K. (2019). Some properties of pentagonal neutrosophic numbers and its applications in transportation problem environment. Infinite Study, 28, 200-215.
Chakraborty, A., Mondal, S., & Broumi, S. (2019). De-neutrosophication technique of pentagonal neutrosophic number and application in minimal spanning tree. Infinite Study, 29, 1-18.
Abdel-Basset, M., Saleh, M., Gamal, A., & Smarandache, F. (2019). An approach of TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing, 77, 438-452. https://doi.org/10.1016/j.asoc.2019.01.035
Deli, I., Ali, M., & Smarandache, F. (2015, August). Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In 2015 International conference on advanced mechatronic systems (ICAMechS) (pp. 249-254). Ieee. https://doi.org/10.1109/ICAMechS.2015.7287068
Nabeeh, N. A., Abdel-Basset, M., El-Ghareeb, H. A., & Aboelfetouh, A. (2019). Neutrosophic multi-criteria decision making approach for IoT-based enterprises. IEEE Access, 7, 59559-59574. https://doi.org/10.1109/ACCESS.2019.2908919
Chakraborty, A., Mondal, S. P., Alam, S., & Mahata, A. (2020). Cylindrical neutrosophic single‐valued number and its application in networking problem, multi‐criterion group decision‐making problem and graph theory. CAAI Transactions on Intelligence Technology, 5(2), 68-77. https://doi.org/10.1049/trit.2019.0083
Rahaman, M., Mondal, S. P., Chatterjee, B., & Alam, S. (2021). The solution techniques for linear and quadratic equations with coefficients as Cauchy neutrosophic numbers. Granular computing, 1-19. https://doi.org/10.1007/s41066-021-00276-0
Kaleva, O. (1987). Fuzzy differential equations. Fuzzy sets and systems, 24(3), 301-317. https://doi.org/10.1016/0165-0114(87)90029-7
Bede, B., & Gal, S. G. (2005). Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy sets and systems, 151(3), 581-599. https://doi.org/10.1016/j.fss.2004.08.001
Allahviranloo, T., Abbasbandy, S., Salahshour, S., & Hakimzadeh, A. (2011). A new method for solving fuzzy linear differential equations. Computing, 92, 181-197. https://doi.org/10.1007/s00607-010-0136-6
Buckley, J. J., & Feuring, T. (2000). Fuzzy differential equations. Fuzzy sets and Systems, 110(1), 43-54. https://doi.org/10.1016/S0165-0114(98)00141-9
Buckley, J. J., & Feuring, T. (2001). Fuzzy initial value problem for Nth-order linear differential equations. Fuzzy sets and systems, 121(2), 247-255. https://doi.org/10.1016/S0165-0114(00)00028-2
Allahviranloo, T., & Ahmadi, M. B. (2010). Fuzzy laplace transforms. Soft computing, 14, 235-243. https://doi.org/10.1007/s00500-008-0397-6
Ghanbari, M. (2012). Solution of the first order linear fuzzy differential equations by some reliable methods. Journal of fuzzy set valued analysis, 2012, 20. https://doi.org/10.5899/2012/jfsva-00126
Rahaman, M., Mondal, S. P., Algehyne, E. A., Biswas, A., & Alam, S. (2021). A method for solving linear difference equation in Gaussian fuzzy environments. Granular Computing, 1-14. https://doi.org/10.1007/s41066-020-00251-1
Rahaman, M., Mondal, S. P., Alam, S., & Goswami, A. (2021). Synergetic study of inventory management problem in uncertain environment based on memory and learning effects. Sādhanā, 46(1), 39. https://doi.org/10.1007/s12046-021-01562-y
Manna, A. K., Rahman, M. S., Shaikh, A. A., Bhunia, A. K., & Konstantaras, I. (2022). Modeling of a carbon emitted production inventory system with interval uncertainty via meta-heuristic algorithms. Applied Mathematical Modelling, 106, 343-368. https://doi.org/10.1016/j.apm.2022.02.003
Garg, H., Sugapriya, C., Kuppulakshmi, V., & Nagarajan, D. (2023). Optimization of fuzzy inventory IoT-size with scrap and defective items under inspection policy. Soft Computing, 27(5), 2231-2250. https://doi.org/10.1007/s00500-022-07804-3
Pattnaik, S., Nayak, M. M., & Kumar, P. (2023). An Inventory Control Model in the Framework of COVID-19 Disruptions Considering Overage Items with Neutrosophic Fuzzy Uncertainty. Neutrosophic Sets and Systems, 56(1), 9.
Mondal, S. P., & Roy, T. K. (2015). System of differential equation with initial value as triangular intuitionistic fuzzy number and its application. International Journal of Applied and Computational Mathematics, 1, 449-474. https://doi.org/10.1007/s40819-015-0026-x
Smarandache, F. (2015). Neutrosophic precalculus and neutrosophic calculus: neutrosophic applications. Infinite Study, 1-156.
Son, N. T. K., Dong, N. P., Long, H. V., & Khastan, A. (2020). Linear quadratic regulator problem governed by granular neutrosophic fractional differential equations. ISA transactions, 97, 296-316. https://doi.org/10.1016/j.isatra.2019.08.006
Sumathi, I. R., & Priya, V. M. (2018). A new perspective on neutrosophic differential equation. International Journal of Engineering & Technology, 7(4.10), 422-425.
Sumathi, I. R., & Antony Crispin Sweety, C. (2019). New approach on differential equation via trapezoidal neutrosophic number. Complex & Intelligent Systems, 5, 417-424. https://doi.org/10.1007/s40747-019-00117-3
Moi, S., Biswas, S., & Pal, S. (2021). Second-order neutrosophic boundary-value problem. Complex & Intelligent Systems, 7, 1079-1098. https://doi.org/10.1007/s40747-020-00268-8
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Scientific Oasis
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
