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In this paper, two kinds of optimality concepts are introduced into fuzzy linear programming problems in order to discuss the rationality of an obtained solution. One is possible optimality evaluating the possibility degree to which the solution is optimal. The other, the dual concept, is necessary optimality evaluating the necessity degree to which the solution is optimal. When possibility distributions are defined by closed intervals, degrees of possible and necessary optimalities become binary. Necessary and sufficient conditions for possible and necessary optimalities are induced in this case. Extending the results, methods of calculating the degrees of possible and necessary optimalities are proposed. Some numerical examples are given to demonstrate the proposed methods.