Fuzzy Solution of Z-Number-Based Multi-Objective Linear Programming Models with Different Membership Functions

In real-world decision-making, uncertainty plays a crucial role, especially when dealing with complex, multi-objective optimization problems. Traditional linear programming (LP) models often have the assumption that the data is precise and deterministic. However, this ‎assumption is often not realistic for many applications, as imprecision will always be present. This paper presents a fuzzy solution to ‎Z-Z-number-based multi-objective linear programming (ZMOLP) models. Z-numbers can combine fuzzy logic and Z-numbers to manage ‎uncertainty in (multi-objective) decision dilemmas. A Z-number consists of two parts: a fuzzy number for the uncertainty in the ‎data and a reliability score that indicates the degree of confidence in the data. The two aspects of Z-numbers make them ef‎fective for modeling imprecise data in multi-objective positioning. The effectiveness and overall computational efficiency of different ‎fuzzy membership functions (triangular, trapezoidal, Gaussian, etc.) were also explored to understand their impact on optimal solu‎tions. Z-numbers, through fuzzy numbers, provide a flexible and adaptable decision-making solution far superior to traditional methods ‎for managing imprecision that leads to a better representation of uncertainty related to objectives and constraints. To demonstrate the viability of Z-number-based approaches, practical applications were employed to illustrate their usage in healthcare decision-making and ‎engineering optimization‎.