Motivated by Chernoff’s bound on asymptotic probability of error we propose the alpha-divergence measure and a surrogate, the alpha-Jensen difference, for feature classification, indexing and retrieval in image and other databases. The alpha-divergence, also known as Renyi divergence, is a generalization of the Kullback-Liebler divergence and the Hellinger affinity between the probability densi...

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...

Let $ f: {\mathcal H} \rightarrow \mathbb{R} be a convex differentiable function whose solution set {{\rm{argmin}}}\; f is nonempty. To attain of the problem \min_{\mathcal H}f $, we consider second order dynamic system \;\ddot{x}(t) + \alpha \, \dot{x}(t) \beta (t) \nabla f(x(t)) c x(t) = 0 where positive such that \lim_{t\rightarrow +\infty}\beta(t) +\infty $. By imposing adequate hypothesis ...