A generalized parametric approach for solving different fuzzy parameter based multi-objective transportation problem

This research article presents a novel two-step generalized parametric approach to address various fuzzy parameter-based multi-objective transportation problems. These problems involve uncertain or imprecise data, making it challenging to find precise solutions. This research article aims to find multiple optimal solutions for various values of the parameter μ∈[0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \in [0,1]$$\end{document}, ultimately giving decision-makers a range of options from which the final solution is to choose. The suggested methodology consists of two main steps. In the first step, the fuzzy data is partitioned into distinct split levels using parametric equations controlled by the precision parameter μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}, thereby transforming the FMOTPs into CMOTPs. In the second step, fuzzy programming techniques are employed to solve the CMOTPs for varying values of μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu $$\end{document}, generating multiple optimal solutions. The gray relational analysis (GRA) technique is utilized within each split level to identify the best optimal compromise solution for that specific level. Furthermore, the preferred compromise solution is selected based on its minimal Euclidean distance to the ideal solution across all split levels, offering additional insights for decision-making. The proposed method is illustrated on three numerical problems, demonstrating its effectiveness in providing a range of trade-offs between conflicting objectives. A comparative analysis with existing methods in the literature highlights the advantages of the proposed approach, showcasing its practical usefulness in real-world transportation decision-making processes.