Interactive Approach for Multi-Level Multi-Objective Fractional Programming Problems with Fuzzy Parameters

In this paper, an interactive approach for solving multi-level multi-objective fractional programming (ML-MOFP) problems with fuzzy parameters is presented. The proposed interactive approach makes an extended work of Shi and Xia (1997). In the first phase, the numerical crisp model of the ML-MOFP problem has been developed at a confidence level without changing the fuzzy gist of the problem. Then, the linear model for the ML-MOFP problem is formulated. In the second phase, the interactive approach simplifies the linear multi-level multi-objective model by converting it into separate multi-objective programming problems. Also, each separate multi-objective programming problem of the linear model is solved by the ∊-constraint method and the concept of satisfactoriness. Finally, illustrative examples and comparisons with the previous approaches are utilized to evince the feasibility of the proposed approach.