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In this paper, we discuss the softness and the robustness of the optimality in the setting of linear programming problems with a fuzzy objective function. A fuzzy goal defined on the deviation from the optimal value is introduced in order to define the soft-optimal solution. Fuzzy coefficients are regarded as possibility distributions. A necessity measure based on the possibility distribution is used for defining a necessarily optimal solution, i.e., a robust-optimal solution. Since a necessarily optimal solution does not exist in many cases, a necessarily soft-optimal solution is defined. A solution algorithm for the best necessarily soft-optimal solution is proposed.