Abstract: To deal with the uncertainty of the data for input and/or output in the real world, many experts presented efficiency interval to evaluate the performance for each DMU from optimistic and pessimistic views. Undeniably, the lower and upper bound of the efficiency interval are two extremes of each DMU performance. In this paper, the preference of the decision makers are considered by introducing the attitude index to get the most probable efficiency value, which with the lower and upper bound constitutes the ternary efficiency interval. Then ternary directional distance index is proposed, improving the two-grade ranking method, to get a full ranking for all DMUs. The illustrative example shows this method is more precise and widely used in efficiency evaluation and decision-making field.the effectiveness and practicability of the proposed method.

Key words: data envelopment analysis, ternary efficiency interval, optimistic efficiency, pessimistic efficiency, ternary directional distance index