1
Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia; Department of Operations and Management Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
(Ha.Ahmed@qu.edu.sa)
2
Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq
(faisal.ghazi@uoanbar.edu.iq)
3
Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia
(aalquran@kfu.edu.sa)
4
Department of Mathematics, Jamoum University College, Umm Al-Qura University, Makkah, Saudi Arabia
(amhalgarni@uqu.edu.sa)
5
Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Mataram, Mataram, 83125, Indonesia
(mamika@unram.ac.id)
6
Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia 9MEU Research Unit, Middle East University, Amman, Jordan
(zahari@uitm.edu.my)
7
Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia; MEU Research Unit, Middle East University, Amman, Jordan; Applied Science Research Center, Applied Science Private University, Amman 11931, Jordan
(aalkhassawneh@kfu.edu.sa)
Abstract :
The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.
Keywords :
Optimization; Multiobjective dynamic programming; Fuzzy set; Piecewise quadratic fuzzy numbers; Close interval approximation; pareto optimal solution; Decision making; Stability; Neutrosophic numbers; Score function
References :
[1] Bellman, R. E. Dynamic Programming, Princeton University Press, Princeton, N. J., 1957.
[2] Mine, H., and Fukushima, M. (1979). Decomposition of multiple criteria mathematical programming by dynamic programming. International Journal of Systems Science, 10(5): 557- 566.https://doi.org/10.1080/00207727908941602.
[3] Carraway, R. L., Morin, Th.., and Moskowitz, H. (1990). Generalized dynamic programming for multicritera optimization. European Journal of Operational Research, (44):95-104.https://doi.org/10.1016/0377-2217(90)90318-6.
[4] Abo- Sinna, M. A., Hussein, M. L. (1995). An algorithm for generating efficient solutions of multiobjective dynamic programming problems. European Journal of Operational Research, (80):156-165.
[5] Osman, M. S. A, (1977). Qualitative analysis of basic notions in parametric convex programming, I (parameters in the constraints), Aplikace Mat., (22):318- 332.
[6] Osman, M. S. A, (1977). Qualitative analysis of basic notions in parametric convex programming, II (parameters in the objective functions), Aplikace Mat., (22): 333- 348.
[7] Osman, M.S. A., and Dauer, J. P. Characterization of Basic Notations in Multiobjective Convex Programming Problems. Technical Report, Lincoln, University of Nebraska, USA, 1983.
[8] Zadeh, L. A. (1965). Fuzzy sets. Information Control, (8): 338- 353.http://dx.doi.org/10.1016/S0019-9958(65)90241-X.
[9] Bellmann, R., and Zadeh,L. (1970). Decision making in a fuzzy environment. Management Science, (17):141- 164.https://doi.org/10.1287/mnsc.17.4.B141.
[10] Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and System, 1(1): 45–55.http://dx.doi.org/10.1016/0165-0114(78)90031-3.
[11] Dubois, D., and Prade, H. Fuzzy Sets and Systems; Theory and Applications, Academic Press, New York, 1980.
[12] Kaufmann, A., and Gupta, M.M. Fuzzy Mathematical Models in Engineering and Management Science, Elsevier Science Publishing Company INC, New York, 1988.
[13] Zimmermann, H. J. Fuzzy Set Theory and its Applications, (International Series in Management Science/ Operations Research), Kluwer- Nijhoff Publishing, Dordrecht, 1985.
[14] Esogbue, A. O., and Bellman, R. E. (1984). Fuzzy dynamic programming and it is extensions, in H- J. Zimmermann et al., Eds, Times/ Studies in the Management Sciences, (200): 147- 167.
[15] Hussein, M. L., and Abo- Sinna, M. A.(1993). Decomposition of multiobjective programming problems by hybrid fuzzy- dynamic programming. Fuzzy Sets and Systems, (60): 25- 32.
[16] Tanaka, H., and Asai, K. (1984). Fuzzy linear programming with fuzzy numbers. Fuzzy Sets and Systems, 13(1): 1-10.https://doi.org/10.1016/0165-0114(84)90022-8.
[17] Orlovski, S. (1984). Multiobjective programming problems with fuzzy parameters. Control Cybernetic, 13(3): 175- 183
[18] Al-Quran, A., Al-Sharqi, F., Ullah, K., Romdhini, M. U., Balti, M. & Alomai, M., Bipolar fuzzy hypersoft set and its application in decision making. International Journal of Neutrosophic Science, 20, 65-77. 2023
[19] A. Al Quran, A. G. Ahmad, F. Al-Sharqi, A. Lutfi, Q-Complex Neutrosophic Set, International Journal of Neutrosophic Science, vol. 20(2), pp.08-19, 2023.
[20] F. Al-Sharqi, M. U. Romdhini, A. Al-Quran, Group decision-making based on aggregation operator and score function of Q-neutrosophic soft matrix, Journal of Intelligent and Fuzzy Systems, vol. 45, pp.305–321, 2023.
[21] Sakawa, M., and Yano, H. (1989). Interactive decision making for multiobjective nonlinear programming problems with fuzzy parameters, Fuzzy Sets and Systems, 29(3): 315- 326.https://doi.org/10.1016/0165-0114(89)90043-2.
[22] Sakawa, M., and Yano, H.(1990). An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy parameters. Fuzzy Sets and Systems, (30): 221- 238.
[23] Osman, M. S. A., and El- Banna, A. H. (1993). Stability of multiobjective nonlinear programming problems with fuzzy parameters'', Mathematics and Computers in Simulation, (35): 321- 326.
[24] Moghaddam- J,A. R., and Ghoseiri, K. (2011). Fuzzy dynamic multi- objective Data Envelopment Analysis model. Expert Systems with Applications, 38(1): 850-855. https://doi.org/10.1016/j.eswa.2010.07.045.
[25] F. Al-Sharqi, Y. Al-Qudah and N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets. Neutrosophic Sets and Systems, 55(1) (2023), 358-382.
[26] F. Al-Sharqi, A. Al-Quran, M. U. Romdhini, Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment, Iraqi Journal for Computer Science and Mathematics, vol. 4, pp.18–29, 2023.
[27] M. U. Romdhini, F. Al-Sharqi, A. Nawawi, A. Al-Quran and H. Rashmanlou, Signless Laplacian Energy of Interval-Valued Fuzzy Graph and its Applications, Sains Malaysiana 52(7), 2127-2137, 2023.
[28] Z. bin M. Rodzi et al. Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia, Int. J. Neutrosophic Sci., vol. 21, no. 3, pp. 106–114, 2023.
[29] Muruganantham, A., Zhao, Y., Gee, S. B., Qiu, X., and Tan, K. C. (2013). Dynamic multiobjective optimization using evolutionary algorithm with Kalman Filter. Procedia Computer Science, (24): 66- 75. https://doi.org/10.1016/j.procs.2013.10.028.
[30] Li, Z., Chen, H., Xie, Z., Chen, C., and Sallam. A. (2014). Dynamic multiobjective optimization algorithm based on average distance linear predication model. The Scientific World Journal, Vol. 2014, Article ID389742, 9 pages. . https://doi.org/10.1155/2014/389742.
[31] Deng, X., Xu, W- J., and Wang, Z- Q. (2016). Dynamic multi- objective fuzzy portfolio model that considers corporate social responsibility and background risk. Journal of Interdisciplinary Mathematics, 19(2): 413- 432. https://doi.org/10.1080/09720502.2015.112286.
[32] Besheli, S. F., Keshteli, R. N., Emami, S., and Rasoluli, S. M. (2017). A fuzzy dynamic multi- objective multi- item model by considering customer satisfaction in a supply chain. Scientia Iranica E, 24(5): 2623- 2639. https://doi: 10.24200/sci.2017.4392.
[33] Peraza, C., Valdez, F., Castro, J. R., and Castillo, O. (2018). Fuzzy dynamic parameter Adaptation in the harmony search algorithm for the optimization of the ball and beam controller. Advances in Operations Research, Vol. 2018, Article ID 3092872, 16 pages. https://doi.org/10.1155/2018/3092872.
[34] Azevedo, M. M., Crispim, J. A., and de Sousa,J. P. (2019). A dynamic multiobjective model for designing machine layouts. IFAC- PapersOnLine, 52(13): 1896- 1901. https://doi.org/10.1016/j.ifacol.2019.11.479.
[35] Ni, P., Gao, J., Song, Y., Quan, W., and Xing, Q. (2020). A new method for dynamic multi- objective optimization based on segment and cloud prediction. Symmetry, (12): 465- 477. http://dx.doi.org/10.3390/sym12030465.
[36] Wu, Y., Shi, L., and Liu, X. (2020). A new dynamic strategy for dynamic multiobjective optimization. Information Sciences, (529): 116- 131.https://doi.org/10.1016/j.ins.2020.04.011.
[37] Liu, R., Yang, P., and Liu, J. (2021). A dynamic multi- objective optimization evolutionary algorithm for complex environmental changes. Knowledge- Based Systems, (216): 106612. https://doi.org/10.1016/j.knosys.2020.106612.
[38] Zou, F., Yen, G. G., and Zhao, C. (2021). Dynamic multiobjective optimization driven by inverse reinforcement learning. Information Sciences, (575): 468- 484. https://doi.org/10.1016/j.ins.2021.06.054.
[39] Zhang, Q., Jiang, S., Yang, S., and Song, H. (2021). Solving dynamic multi- objective problems with a new prediction- based optimization algorithm. PloS One, 16(8): e0254839. doi: 10.1371/journal.pone.0254839. eCollection 2021.
[40] Mena, R., Godoy, M., Catalan, C., Viveros, P., and Zio, E. (2023). Multi- objective two- stage stochastic unit commitment model for win- integrated power systems : A compromise programming approach. International Journal of Electrical Power&Energy systems, (152): 109214.
[41] Wu, F., Wang, W., Chen, J., and Wang, Z. (2023). A dynamic multi- objective optimization method based on classification strategies. Scientific Reports, (13): 15221.
[42] Jain, S. (2010). Close interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program. Iranian Journal of Operations Research, 2(1): 77- 88.
[43] Atanason, K. T.(1986), '' Intuitionistic fuzzy sets'', Fuzzy Sets and Systems, Vol. 20 , pp.87- 96.
[44] Thamaraiselvi, A., and Santhi, R.,'' A new approach for optimization of real life transportation problem in neurosophic environment,'' Mathematical Problems in Engineering, vol. 2016, Article ID 5950747,9 pages.
[45] Rockafellar, R.(1967). Duality and stability in extermal problems involving convex functions. Pacific Journal of Mathematics, (21): 167- 181.https://doi.org/10.2140/PJM.1967.21.167.
[46] Chankong, V., and Haimes, Y. Y. Multiobjective Decision Making Theory and Methodology, North- Holland, New York, 1983.
[47] Mangasarian, O. L. Nonlinear Programming, McGraw- Hill, New York, 1969.
[48] Zeleny, M. Linear Multiobjective Programming, Lecture Notes in Economics and Mathematical Systems, Vol. 95,Springer- Verlag, New York, 1974.http://dx.doi.org/10.1016/0165-0114(78)90031-3.
| Style | # |
|---|---|
| MLA | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi. "Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems." International Journal of Neutrosophic Science, Vol. 23, No. 1, 2024 ,PP. 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |
| APA | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi. (2024). Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |
| Chicago | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi. "Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems." Journal of International Journal of Neutrosophic Science, 23 no. 1 (2024): 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |
| Harvard | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi. (2024). Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems. Journal of International Journal of Neutrosophic Science, 23 ( 1 ), 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |
| Vancouver | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi. Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 1 ): 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |
| IEEE | Hamiden Abd El- Wahed Khalifa, Faisal Al-Sharqi, Ashraf Al-Quran, Aziza Algarni, Mamika Ujianita Romdhini, Zahari Rodzi, Abdalwali Lutfi, Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 1 , (2024) : 299-310 (Doi : https://doi.org/10.54216/IJNS.230125) |