A novel Fuzzy Entropy based on the Non-Extensive entropy and its application for feature selection

A novel Fuzzy Entropy is defined in this work that is based on the recently proposed probabilistic Non-Extensive entropy for correlated texture patterns. The main reason behind the success of the Non-Extensive entropy was its nonlinear one-sided Gaussian Information Gain function which is non-additive and hence is suitable for representing correlated data structures. The properties of the new fuzzy entropy are found to satisfy the basic properties set in literature for fuzzy entropies. In addition the feature selection using the proposed fuzzy entropy is also discussed along with its merits. It is specially noted that the fuzzy version of the non-extensive entropy retains its non-additivity property for crisp values of the membership function.