Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems
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 div...
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2025-04-01
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| author | Mohamed A. El Sayed Farahat A. Farahat Mohamed A. Elsisy Maazen Alsabaan Mohamed I. Ibrahem Haitham Elwahsh |
| author_facet | Mohamed A. El Sayed Farahat A. Farahat Mohamed A. Elsisy Maazen Alsabaan Mohamed I. Ibrahem Haitham Elwahsh |
| author_sort | Mohamed A. El Sayed |
| collection | DOAJ |
| description | 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. |
| format | Article |
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| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-a2fdc88a81c848648f267b7b8454dded2025-08-20T02:28:15ZengMDPI AGMathematics2227-73902025-04-01138124210.3390/math13081242Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming ProblemsMohamed A. El Sayed0Farahat A. Farahat1Mohamed A. Elsisy2Maazen Alsabaan3Mohamed I. Ibrahem4Haitham Elwahsh5Basic Sciences Department, Faculty of Engineering, BADR University in Cairo BUC, Cairo 11829, EgyptHigher Technological Institute, Tenth of Ramadan City 44629, EgyptDepartment of Basic Engineering Sciences, Faculty of Engineering, Benha University, Banha 13511, EgyptDepartment of Computer Engineering, College of Computer and Information Sciences, King Saud University, P.O. Box 51178, Riyadh 11543, Saudi ArabiaSchool of Computer and Cyber Sciences, Augusta University, Augusta, GA 30912, USAFaculty of Information Technology, Applied Science Private University, Amman 11931, JordanThe 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.https://www.mdpi.com/2227-7390/13/8/1242bi-level optimizationmulti-objective programmingmulti-choice programmingrough setTOPSIS |
| spellingShingle | Mohamed A. El Sayed Farahat A. Farahat Mohamed A. Elsisy Maazen Alsabaan Mohamed I. Ibrahem Haitham Elwahsh Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems Mathematics bi-level optimization multi-objective programming multi-choice programming rough set TOPSIS |
| title | Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems |
| title_full | Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems |
| title_fullStr | Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems |
| title_full_unstemmed | Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems |
| title_short | Two TOPSIS-Based Approaches for Multi-Choice Rough Bi-Level Multi-Objective Nonlinear Programming Problems |
| title_sort | two topsis based approaches for multi choice rough bi level multi objective nonlinear programming problems |
| topic | bi-level optimization multi-objective programming multi-choice programming rough set TOPSIS |
| url | https://www.mdpi.com/2227-7390/13/8/1242 |
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