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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.

Study on probabilistic multi- objective linear fractional programming problems under fuzziness