Solving Fully Intuitionistic Fuzzy Multi-Level Multi-Objective Fractional Optimization Problems via Two Different Approaches

Uncertainty is the biggest issue when modeling real-world multi-level fractional optimization problems. In this paper, a fully intuitionistic fuzzy multi-level multi-objective fractional programming problem (FIF-MLMOFPP) is tackled via two different approaches. Because of the ambiguity introduced in the model, all the parameters and decision variables in each objective function and feasible domain are intuitionistic fuzzy numbers (IFNs). Firstly, FIF-MLMOFPP is converted into a non-fractional fully intuitionistic fuzzy multi-level multi-objective programming problem (FIF-MLMOPP) utilizing a series of transformations. The accuracy functions and ordering relations of IFNs are employed to transform the non-fractional FIF-MLMOPP into a deterministic variant. An interactive approach is first applied to solve the problem by transforming it into discrete multi-objective optimization problems (MOOPs). Each separate MOOP addresses the ϵ-constraint methodology and the goal of satisfactoriness. Neutrosophic fuzzy goal programming (NFGP) is the second approach applied to solve the FIF-MLMOFPP, as the marginal evaluations of predetermined neutrosophic fuzzy objectives for all functions at each level are attained through various membership functions, including degrees of truth, indeterminacy, and falsehood, within neutrosophic uncertainty. The NFGP algorithm is presented to achieve optimal levels for each marginal evaluation objective by minimizing their deviation variables, thus yielding a suitable solution. To confirm and approve the two suggested approaches, a numerical example and a comparison between them are presented. Finally, recommendations for additional research are given.