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Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems

Author

Listed:
  • Mohamed A. El Sayed

    (Basic Sciences Department, Faculty of Engineering, BADR University in Cairo BUC, Cairo 11829, Egypt
    Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, Banha 13511, Egypt)

  • Farahat A. Farahat

    (Higher Technological Institute, Tenth of Ramadan City 44629, Egypt)

  • Mohamed A. Elsisy

    (Department of Basic Engineering Sciences, Faculty of Engineering, Benha University, Banha 13511, Egypt)

  • Maazen Alsabaan

    (Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, P.O. Box 51178, Riyadh 11543, Saudi Arabia)

  • Mohamed I. Ibrahem

    (School of Computer and Cyber Sciences, Augusta University, Augusta, GA 30912, USA)

  • Haitham Elwahsh

    (Faculty of Information Technology, Applied Science Private University, Amman 11931, Jordan
    Department of Computer Science, Faculty of Computers and Information, Kafrelsheikh University, Kafrelsheikh 33516, Egypt)

Abstract

The multi-choice rough bi-level multi-objective nonlinear programming problem (MR-BLMNPP) has noticeably risen in various real applications. In the current model, the objective functions have a multi-choice parameter, and the constraints are represented as a rough set. In the first phase, Newton divided differences (NDDs) are utilized to formulate a polynomial of the objective functions. Then, based on the rough set theory, the model is converted into an Upper Approximation Model (UAM) and Lower Approximation Model (LAM). In the second phase, two Technique of Order Preferences by Similarity to Ideal Solution (TOPSIS)-based models are presented to solve the MR-BLMNPP. A TOPSIS-based fuzzy max–min and fuzzy goal programming (FGP) model are applied to tackle the conflict between the modified bi-objective distance functions. An algorithm for solving MR-BLNPP is also presented. The applicability and efficiency of the two TOPSIS-based models suggested in this study are presented through an algorithm and a numerical illustration. Finally, the study presents a bi-level production planning model (BL-PPM) as an illustrative application.

Suggested Citation

  • Mohamed A. El Sayed & Farahat A. Farahat & Mohamed A. Elsisy & Maazen Alsabaan & Mohamed I. Ibrahem & Haitham Elwahsh, 2025. "Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems," Mathematics, MDPI, vol. 13(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1242-:d:1631465
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    References listed on IDEAS

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    1. M. A. El Sayed & Ibrahim A. Baky & Pitam Singh, 2020. "A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1374-1403, December.
    2. Arora, S.R. & Gupta, Ritu, 2009. "Interactive fuzzy goal programming approach for bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 194(2), pages 368-376, April.
    3. S. H. Nasseri & S. Bavandi, 2020. "Multi-choice Linear Programming in Fuzzy Random Hybrid Uncertainty Environment and Their Application in Multi-commodity Transportation Problem," Fuzzy Information and Engineering, Taylor & Francis Journals, vol. 12(1), pages 109-122, January.
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    6. Hadeel Al Qahtani & Ali El–Hefnawy & Maha M. El–Ashram & Aisha Fayomi, 2019. "A Goal Programming Approach to Multichoice Multiobjective Stochastic Transportation Problems with Extreme Value Distribution," Advances in Operations Research, Hindawi, vol. 2019, pages 1-6, September.
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