The concept of set was introduced by L. A. Zadeh in 1965. This concept is considered to provide a new way for handling intrinsic ambiguity by a different view point from statistical treatment. Some relations between the fuzziness and the concept of entropy, an original description of vagueness, have been first studied by DeLuca-Termini and its several variations have been introduced by Knopfmacher, Ebanks and others. In this paper, we introduce the fuzzy relative expressing the relative amount of fuzziness between two sets based on the Kullback-Leibler information in probability theory and study its properties. In particular, a characterization theorem of the relative entropy is shown.