Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

Hamiden Abd El- Wahed; Faisal; Ashraf; Zahari; Heba Ghareb; Abdalwali

doi:https://doi.org/10.54216/IJNS.230120

Full Length Article

Volume 23 • Issue 1 • PP: 287-298 • 2024

Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

Hamiden Abd El- Wahed Khalifa ^1*

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,

Faisal Al-Sharqi ²

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,

Ashraf Al-Quran ³

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,

Zahari Rodzi ⁴

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,

Heba Ghareb Goma ⁵

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,

Abdalwali Lutfi

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¹Department 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 St

²Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq

³Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia

⁴College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia

⁵Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt

⁶Department 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,

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.230120

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Received: May 27, 2023 Revised: August 11, 2023 Accepted: November 26, 2023

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Abstract

In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right- hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non- linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology.

Keywords

Optimization neutrosophic set single valued neutrosophic numbers Chance- constrained programming Bi- level linear programming Decision Making Normal distribution Joint constraints Incomplete Gamma function &nbsp Membership function Fuzzy programming approach Optimal compromise solution

References

[1] Dempe, S. Foundations of bilevel Programming, Kluwer Academic, Dordrecht, Netherlands, 2002.

[2] Dempe, S. (2003). Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization, 52(3): 333- 359.

[3] Colson, B., Marcotte, P., and Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research 153(1): 235- 256.

[4] Gzara, F. (2013). A cutting plane approach for bilevel hazardous material transport network design. Operations Research Letters, 41(1): 40-46.

[5] Fontaine, P., and Minner, S. (2014). Benders decomposition for discrete- continuous linear bilevel problems with application to traffic network design. Transportation Research Part B: Methodological,(70): 163- 172.

[6] Cecchini, M., Ecker, J., Kupferschmid, M., and Leitch, R. (2013). Solving nonlinear principle- agent problems using bilevel programming. European Journal of Operational Research, 230(2): 364- 373.

[7] Zhang, G., Zhang, G., Gao, Y., and Lu, J. (2011). Competitive strategic bidding optimization in electricity markets using bilevel programming and swarm technique. IEEE Transactions on Industrial Electronics, 58(6): 2138-2146.

[8] Bialas, W.F., and Karwan, M. H. (1982). On two- level optimization, IEEE Transaction Automatic Control, AC-27, 211-214.

[9] Bialas, W.F., and Karwan, M. H. (1982). Two- level linear programming. Management Science, (30): 1004- 1020.

[10] Bard, J. F., and Falk, J.E. (1982). An explicit solution to the multi- level programming problem. Computers Operations Research, (9): 77- 100.Applications, Kluwer Academic Publisers, Dordrecht, The Netherlands, 1998.

[11] Anandalingam, G. (1988). A mathematical programming model of decentralized multi- level systems. Journal of Operational Research Society, 39(11): 1021- 1033.

[12] Shih, H- S., Lai, Y- J., and Lee, E. S.(1996). Fuzzy approach for multi- level programming problems. Computers Operations Research, 23(1): 73- 91.

[13] Ye, J. J., and Zhu, D. L. (1995). Optimality conditions for bi- level linear programming problems. Optimization, 33(1): 9- 27.

[14] Chen, Y., and Florian, M. (1995). The non- linear bi- level programming problem: Formulations, regularity and optimality conditions, Optimization, 32(3): 193- 209.

[15] Falk, J. E., and Liu, J. (1995). On bi- level programming I: General nonlinear cases. Mathematical Programming, 70(1): Ser A, 47- 72.

[16] Gendreau, M. Marcotte, P., and Savard, G. (1996). A hybrid Tabu- Ascent algorithm for the linear bilevel programming problem. Journal of Operational Research Society, (32): 783- 792.

[17] Dempe, S.., and Schemidt, H. (1996). On an algorithm solving 2- level programming problems with non- unique lower level solutions. Computers& Optimization Applications, 6(3): 227- 249.

[18] Safaei, N., and Saraj, M. (2014). A new method for solving fully fuzzy linear bi-level programming problems. International Journal of Applied Operational Research, 4(1): 39- 46.

[19] Ren, A. (2015). A novel method for solving the fully fuzzy bi-level linear programming problem. Mathematical Problems in Engineering, vol.2015, Article ID, 11 pages.

[20] Ren, A. (2016). Solving the fully fuzzy bilevel programming problem through deviations degree measures and a ranking function method. Mathematical Problems in Engineering, vol. 2016, Article ID 7069804, II pages. Doi.org/10.1155/2016/7069804.

[21] Hammad, A. W.A. (2019). A bilevel multiobjective optimization approach for solving the evacuation location assignment problem. Advanced in Civil Engineering, vol.2019, Article ID 6052931, 11 pages. Doi.org/10.1155/2019/6052931.

[22] Tahernejad, S., Ralphs, T.K., and DeNeger, S.T. (2020). A branch- and – cut algorithm for integer bilevel linear optimization problems and its implementation. Mathematical Programming Computation, doi.org/10.1007/s12532-020-00183-6.

[23] Rey, D. (2020). Computational benchmarking of exact method for the bilevel discrete network design problem. Transportation Research Procedia, (47): 11-18. Doi.org/10.1016/j.trpro.2020.03.67.

[24] Sengupta, J. K. Stochastic Programming: Methods and Applications, North- Holland Publishing Company, 1972.

[25] Goicoechea, A., Don, R. Hansen and Lucien Duckstein. Multiobjective Decision Analysis with Engineering and Business Applications, John Wiley& Sons, 1982.

[26] Leberling, H. (1981). On finding compromise solution in multi- criteria problems using the min- operator. Fuzzy Sets and Systems, (10): 33-41

[27] Teghem, J. Jr., Dufrance, D., Thauvoye, M., and Kunch, P. (1986). An interactive method for multiobjective linear programming under uncertainty. European Journal of Operations Research, (26): 65- 82.

[28] Sinha, S. B., Biswal, M.P., and Hulsurkar, S. (1998). Fuzzy programming to the multi- objective probabilistic linear programming problems when only are probabilistic. The Journal of Fuzzy Mathematics, 6(1): 63- 73.

[29] Zadeh, L. A. (1965). Fuzzy sets. Information Control, 8(3): 338-353.

[30] Dubois, D., and Prade, H. Fuzzy sets and systems: theory and applications, Academic Press, New York, 1980.

[31] Bellman, R. E., and Zadeh, L.A. (1970). Decision making in a fuzzy environment. Management Science, (17): 141- 164.

[32] Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and System, 1(1): 45–55.

[33] Narasiman, R. (1980). Goal programming in a fuzzy environment. Decision Sciences, (11): 325- 336.

[34] 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.

[35] 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.

[36] 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

[37] 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.

[38] Zimmermann, H-J. Fuzzy Set Theory and its Applications, Kluwer- Nijhoff Publishing, USA, 1985.

[39] Sinha, S., and Biswal, M.P. (2000). Fuzzy programming approach to bi- level linear programming problems. The Journal of Fuzzy Mathematics, 8(2): 337- 347.

[40] 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.

[41] Camacho- Vallejo, Corpus, C., and Villegas, J. (2024). Metaheuristics for bilevel optimization: A comprehensive review. Computers& Operations Research, (161): 106410.

[42] Atanassov, K. T. (1986). Instuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1): 87- 96.

[43] Smarandache, F. A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Lgics, American Research Press, Reoboth, NM, USA, 1998.

[44] Wang, H., Smarandache, F., Zhang, Y. Q., and Sunderraman, R. (2010). Single valued neutrosophic sets. Multistructure, (4): 410-413.

[45] Wang, J., Nie, R., Zhang, H., and Chen, X. (2013). New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis. Information Sciences, (251): 69- 95.

[46] Sinha, S.B., Hulsurkar, S., Biswal, M. P. (2000). Fuzzy programming approach to multi- objective stochastic problems when follow joint normal distribution. Fuzzy Sets and Systems, (109): 91- 96.

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Khalifa, Hamiden Abd El- Wahed, Al-Sharqi, Faisal, Al-Quran, Ashraf, Rodzi, Zahari, Goma, Heba Ghareb, Lutfi, Abdalwali. "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 1, 2024, pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, H., Al-Sharqi, F., Al-Quran, A., Rodzi, Z., Goma, H., Lutfi, A. (2024). Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution. International Journal of Neutrosophic Science, Volume 23(Issue 1), 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, Hamiden Abd El- Wahed, Al-Sharqi, Faisal, Al-Quran, Ashraf, Rodzi, Zahari, Goma, Heba Ghareb, Lutfi, Abdalwali. "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution." International Journal of Neutrosophic Science Volume 23, no. Issue 1 (2024): 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, H., Al-Sharqi, F., Al-Quran, A., Rodzi, Z., Goma, H., Lutfi, A. (2024) 'Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution', International Journal of Neutrosophic Science, Volume 23(Issue 1), pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa H, Al-Sharqi F, Al-Quran A, Rodzi Z, Goma H, Lutfi A. Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 1):287-298. DOI: https://doi.org/10.54216/IJNS.230120

H. Khalifa, F. Al-Sharqi, A. Al-Quran, Z. Rodzi, H. Goma, A. Lutfi, "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 1, pp. 287-298, 2024. DOI: https://doi.org/10.54216/IJNS.230120

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