Uncertainties and fuzziness are basic phenomena in human thinking and in many real-world objectives. In the existing literature of information theory various divergence measures are available for studying such phenomena in accordance to their ethos. In general, some are probabilistic and some are non-probabilistic by nature. In the present communication, an attempt is made to introduce non-probabilistic divergence measures for fuzzy matrices that are exponential in nature. In the present study, we prove their validity and study their properties. The different applications of proposed non-probabilistic measure are discussed in the amphitheater of decision making and feature selection.