AbstractIn order to handle multiobjective linear programming problems containing fuzzy parameters, the authors have already proposed four kinds of α‐feasibility and β‐Pareto optimality, based on the four kinds of index introduced by Dubois et al. This paper discusses the proposed concepts of four kinds of β‐Pareto optimality in further detail, in order to indicate problems with β‐Pareto optimality. As a means of coping with those problems, four kinds of γ‐Pareto optimal solutions are introduced. Then the concept of (α, γ)‐Pareto optimal solution is introduced, by considering simultaneously the α‐feasibility and the γ‐Pareto optimality. It is shown that the set of (α, γ)‐Pareto optimal solutions, which can be regarded as the most optimistic and the most pessimistic, can be found using linear programming.