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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 23 , Issue 1 , PP: 287-298, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

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 * , Faisal Al-Sharqi 2 , Ashraf Al-Quran 3 , Zahari Rodzi 4 , Heba Ghareb Goma 5 , Abdalwali Lutfi 6

  • 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 College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia - (zahari@uitm.edu.my)
  • 5 Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt - (dr.heba@suezmis.edu.eg)
  • 6 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)

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

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

    Cite This Article As :
    Abd, Hamiden. , Al-Sharqi, Faisal. , Al-Quran, Ashraf. , Rodzi, Zahari. , Ghareb, Heba. , 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. , no. , 2024, pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. Al-Sharqi, F. Al-Quran, A. Rodzi, Z. Ghareb, 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, (), 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, Hamiden. Al-Sharqi, Faisal. Al-Quran, Ashraf. Rodzi, Zahari. Ghareb, Heba. 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 , no. (2024): 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. , Al-Sharqi, F. , Al-Quran, A. , Rodzi, Z. , Ghareb, 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 , () , 287-298 . DOI: https://doi.org/10.54216/IJNS.230120
    Abd H. , Al-Sharqi F. , Al-Quran A. , Rodzi Z. , Ghareb 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. (): 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. Al-Sharqi, F. Al-Quran, A. Rodzi, Z. Ghareb, 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, vol. , no. , pp. 287-298, 2024. DOI: https://doi.org/10.54216/IJNS.230120

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