In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand. Based on the $\left(\alpha ,\beta \right)$-cut concept a parametric $\left(\alpha ,\beta \right)$-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain $\left(\alpha ,\beta \right)$-Pareto optimal solution. We investigated the stability set of the first kind (SSFK) corresponding to the solution by extending the Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to crystalize the progressing SSFK for PIF-MOFTP as well as an illustrative numerical example is presented.

In this paper multi-level multi-objective fractional programming problem (ML-MOFP) is considered where some or all of its coefficients in the objective function are rough intervals. At the first phase of the solution approach and to avoid the complexity of the problem, two FP problems with interval coefficients will be constructed. One of these problems was a FP problem where all of its coefficients are lower approximations of the rough intervals and the other problem was a FP problem where all of its coefficients are upper approximations of rough intervals. At the second phase, a membership function was constructed to develop a fuzzy goal programming model for obtaining the satisfactory solution of the multi-level multi-objective fractional programming problem. The linearization process introduced by Pal et al. [1] will be applied to linearize the membership functions.. Finally, a numerical example will be introduced to illustrate the theoretical results.