Uncertainty in linear fractional transportationproblem

In this paper, we study the linear fractional transportation problem with uncertain parameters. after recalling some definitions, concepts and theorems in uncertainty theory we present three approaches for solving this problem. first we consider the expected value of the objective function together with the expectation of satisfying constraints. optimizing the expected value of the objective function with considering chance constrained method for the restrictions is our second approach. in the third approach we add the objective function to the constraints and solve again the problem by chance constrained method. a numerical example is solved by three approaches and their solutions are compared.