Based on logarithm operation, Bhandari and Pal (1993) defined a divergence measure between two fuzzy sets and deduce a fuzzy entropy. On the basis of exponential operation, a new divergence measure is defined and some properties of this divergence measure is discussed. We study the relations between fuzzy entropy, fuzzy Hamming distance, divergence measure defined by Bhandari and Pal (1993), and divergence measure defined in this paper. We obtain quite a general conclusion and solve the problem proposed by Liu Xuecheng (1992). @ 1999 Elsevier Science B.V. All rights reserved.