In this paper, we focus on hierarchical multiobjective linear programming problems with fuzzy domination structures where multiple decision makers in a hierarchical organization have their own multiple objective linear functions together with common linear constraints. After introducing decision powers and the solution concept based on the α‐level set for the fuzzy convex cone Λ which reflects a fuzzy domination structure, we propose a fuzzy approach to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers but also their own preferences for their membership functions. In the proposed method, instead of Pareto optimal concept, a generalized Λα‐extreme point concept is introduced. In order to obtain a satisfactory solution from among a generalized Λα‐extreme point set, an interactive algorithm based on linear programming is proposed, and an interactive processes are demonstrated by means of an illustrative numerical example.