A Novel Approach to Hexagonal Fuzzy Number Ranking in Multi-Objective Fuzzy Linear Programming Problem Solving
Authors: V.Tharakeswari  
Published: January 2025

This paper presents a ranking process based on hexagonal fuzzy numbers (HFNs) applied to linear programming multi-objective problems with fuzzy measurements. By utilizing this ranking method, any fuzzy linear multi-objective programming problem can be converted into a classical value problem, facilitating the determination of a suitable exact solution. This method offers valuable insights for planners operating in uncertain organizational environments. In an society where numerous opportunities and variables such as manufacturing, inventory, commercial management, costing, and miscellaneous other parameters are involved, this ranking procedure proves to be an efficient approach. The paper includes a computational example to represent the method and provide inferences. Additionally, the well-known Gauss–Seidel iterative method for solving linear systems of equations is discussed.
Introduction: In the realm of linear programming multi-objective problems, decision-makers frequently encounter uncertainty, which can be effectively modelled using fuzzy numbers. Hexagonal fuzzy numbers (HFNs) are particularly adept at representing such uncertainties due to their flexible and detailed structure. The proposed ranking techniques for HFNs provides a systematic approach to convert fuzzy MOLPP into crisp value problems, thereby simplifying the process of finding optimal solutions.
By employing the proposed ranking method, hexagonal fuzzy numbers can be efficiently ranked and compared. This transformation enables the application of traditional optimization techniques to resolve the equivalent crisp problem. A suitable example further illustrates the practical application of this method, demonstrating its effectiveness in deriving actionable insights in complex decision-making scenarios. The paper incorporates the well-known Gauss–Seidel iterative method for solving linear systems of equations, showcasing its integration with the proposed ranking procedure for enhanced problem-solving capabilities.
Objectives: This paper presents a ranking process based on hexagonal fuzzy numbers (HFNs) applied to linear programming multi-objective problems with fuzzy measurements. By utilizing this ranking method, any fuzzy linear multi-objective programming problem can be converted into a classical value problem, facilitating the determination of a suitable exact solution.
Methods: By employing the proposed ranking method, hexagonal fuzzy numbers can be efficiently ranked and compared. This transformation enables the application of traditional optimization techniques to resolve the equivalent crisp problem. A suitable example further illustrates the practical application of this method, demonstrating its effectiveness in deriving actionable insights in complex decision-making scenarios. The paper incorporates the well-known Gauss–Seidel iterative method for solving linear systems of equations, showcasing its integration with the proposed ranking procedure for enhanced problem-solving capabilities.
Results: Based on the table above, we have achieved identical outcomes using both the current approach and the proposed hexagonal WARI ranking method. This technique minimizes solution ambiguity, offering to management an optimal basis for decisions regarding product production or alternative adjustments. It remains effective even with increased variables and parameters, proving simpler and more efficient than prior methods. Furthermore, its applicability extends seamlessly to numerous input parameters. Compared to the existing ranking method, our proposed hexagonal WARI ranking method is equally optimized.
Conclusion: This method allows for the straightforward conversion of hexagonal fuzzy numbers to crisp numbers. We suggest that this proposed method is both easy to use and an excellent additional ranking method.