In this paper, a new concept of the fuzzy stability set of the first kind for multi-level multi-objective
fractional programming (ML-MOFP) problems having a single-scalar parameter in the objective
functions and fuzziness in the right-hand side of the constraints has been introduced. Firstly, A parametric
ML-MOFP model with crisp set of constraints is established based on the
-cut approach. Secondly, a
fuzzy goal programming (FGP) approach is used to find an
-Pareto optimal solution of the parametric
ML-MOFP problem. Thus, the FGP approach is used to achieve the highest degree of each membership
goal by minimizing the sum of the negative deviational variables. Finally, the fuzzy stability set of the
first kind corresponding to the obtained
-Pareto optimal solution is developed here, by extending the
Karush-Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to
clarify the developed fuzzy stability set of the first for parametric ML-MOFP problem as well as
Illustrative numerical example are presented