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The need of suitable divergence measures arises as they play an important role in the problems related to discrimination and inferences. This communication is intended to introduce one such exponential divergence measure based on well-known exponential entropy introduced by Pal and Pal and its validation. Further, this idea has been generalized to introduce a new exponential divergence measure for intuitionistic fuzzy sets. Besides establishing its validity, some of its major properties are also studied. In addition to this, applications of proposed divergence measure for IFSs are given in medical investigation and pattern recognition.