A Study of Probabilistic Multi-Objective Linear Fractional Programming Problems Under Fuzziness

This paper investigates a multi-objective linear fractional programming problem that involves probabilistic parameters on the right-hand side of constraints. probabilistic parameters are randomly distributed with known means and variances through uniform and exponential distributions. after converting the probabilistic problem into an equivalent deterministic problem, a fuzzy programming approach is applied by defining a membership function. a linear membership function is used for obtaining an optimal compromise solution. the stability set of the first kind without differentiability corresponding to the obtained optimal compromise solution is determined. a solution procedure for obtaining an optimal compromise solution and the stability set of the first kind is presented. finally, a numerical example is given to clarify the practicality and efficiency of the study.