Hamiden Khalifa - Operations Research Department- Faculty of Graduate Studies of Statistical Research- Cairo University
E. E. Ammar - ۲. Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt.

   This paper deals with a multi- objective linear fractional programming problem involving probabilistic parameters in the right- hand side of the constraints. These probabilistic parameters are randomly distributed with known means and variances through the use of 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 being 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 practically and the efficiency of the study.  

Multi-objective linear fractional programming, Uniform distribution, Exponential distribution, Linear membership function, Fuzzy programming, optimal compromise solution, parametric study