An extended mathematical model for solving z-number linear programing problems using additive weighting method based on best-worst method

This study addresses the challenge of uncertainty in decision-making by employing Z-numbers, which provide a more effective representation of human knowledge than traditional fuzzy numbers. A novel approach is proposed by integrating Z-numbers into Multi-Objective Linear Programming (MOLP), utilizing the Best-Worst Method (BWM) and additive weighting techniques. Specifically, a Z-number Linear Programming (ZLP) framework is introduced. This framework represents the parameters as Z-numbers, while the decision variables are modeled as fuzzy numbers. First, the ZLP problem is converted into an MOLP form, followed by applying the additive weighting method based on BWM to obtain the optimal solution. Therefore, this study extends a novel approach using Z-number to solve MOLP based on BWM and additive weighting methods. This research contributes to decision-making by providing a robust tool for analyzing uncertain information. The feasibility and effectiveness of our proposed method are demonstrated through a real-world case study and compared with the approach proposed by Akram et al. [۲۹]. The results show the proposed method outperforms the fuzzy numbers method. Overall, comparing the results of the proposed method with those of the conventional fuzzy numbers showed that Z-numbers optimized the objective function better than fuzzy numbers.

کلیدواژه ها:

multi-objective linear programming ، Z-number ، best-worst method ، Additive weighting techniques ، Decision-making