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Due to the appearance of uncontrollable events in discrete-event systems, one may wish to replace the behavior leading to the uncontrollability of pre-specified language by some quite similar one. To capture this similarity, we introduce metric to traditional supervisory control theory and generalize the concept of original controllability to λ-controllability, where λ indicates the similarity degree of two languages. A necessary and sufficient condition for a language to be λ-controllable is provided. We then examine some properties of λ-controllable languages and present an approach to optimizing a realization.