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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Bibliographic Details
Published in:Mathematics (Basel) Vol. 13; no. 8; p. 1242
Main Authors: El Sayed, Mohamed A., Farahat, Farahat A., Elsisy, Mohamed A., Alsabaan, Maazen, Ibrahem, Mohamed I., Elwahsh, Haitham
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.04.2025
Subjects:
Algorithms
Ambiguity
Approximation
bi-level optimization
Decision making
Fuzzy sets
Goal programming
multi-choice programming
multi-objective programming
Multiple objective analysis
Nonlinear programming
Optimization
Polynomials
Production planning
rough set
Set theory
TOPSIS
Serbia
ISSN:2227-7390, 2227-7390
Online Access:Get full text
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Summary: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.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math13081242