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

Mohamed A. El Sayed (), Farahat A. Farahat, Mohamed A. Elsisy, Maazen Alsabaan, Mohamed I. Ibrahem and Haitham Elwahsh
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Mohamed A. El Sayed: Basic Sciences Department, Faculty of Engineering, BADR University in Cairo BUC, Cairo 11829, 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

Mathematics, 2025, vol. 13, issue 8, 1-23

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.

Keywords: bi-level optimization; multi-objective programming; multi-choice programming; rough set; TOPSIS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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