A two-phase fuzzy approach for solving multi-level decision-making problems

• A two-phase fuzzy goal programming (FGP) approach is developed for MLLP problems.
• The first phase finds the solutions to satisfy decision makers in MLLP problems.
• An adjustment scheme is then proposed to adjust the relative satisfaction.
• Each DM can have the satisfaction degree that meets the requirement for MLLP problems.

This paper develops a two-phase fuzzy goal programming (FGP) approach for multi-level linear programming (MLLP) problems in an uncertain environment. A numerical MLLP model is established based on a confidence level. In the first phase, an FGP model is used to find a solution that reaches the overall satisfaction of all decision-makers (DMs), ensuring that the fuzzy goal of each higher-level DM is more satisfied than those of lower-level DMs. Since the higher-level DM has the direct authority to manage the subordinate DM, an adjustment scheme is provided in the second phase for each higher-level DM, who has the opportunity to increase or decrease the satisfaction degree of their fuzzy goal by changing the relative satisfaction of the lower-level DM compared to that of their higher-level DM. A fuzzy variable of the relative satisfaction containing a set of linguistic terms is provided for these adjustments. The adjustment processes are carried out sequentially, from the top to bottom in the hierarchical decision structure. The proposed FGP model in the second phase considers these sequential adjustments. A numerical example and comparisons with existing methods are used to demonstrate the applicability and performance of the proposed approach.