After generalization of Shannon’s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon’s entropy measure. What is the role of the parameter(s) from application point of view? In the present communication, super additivity and fast scalability of generalized hyperbolic measure [Bhatia and Singh, 2013] of probabilistic entropy as compared to some classical measures of entropy has been shown. Application of a generalized hyperbolic measure of probabilistic entropy in certain situations has been discussed. Also, application of generalized hyperbolic measure of fuzzy entropy in multi attribute decision making have been presented where the parameter affects the preference order.

An approach to develop new measures of fuzzy directed divergence is proposed here. A new measure of fuzzy directed divergence is proposed, and some mathematical properties of this measure are proved. The application of fuzzy directed divergence in image segmentation is explained. The proposed technique minimizes the fuzzy divergence or the separation between the actual and ideal thresholded image.