Similar to fuzzy set on a possibility space, uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Entropy provides a quantitative measurement of the uncertainty associated with an uncertain set. This paper presents a formula for calculating the entropy of an uncertain set via its inverse membership function. Based on the formula, the entropy op...

We obtain entropy formulas for Sinai–Ruelle–Bowen (SRB) measures with finite given by inducing schemes. In the first part of work, we Pesin formula class noninvertible systems whose SRB are Gibbs-Markov induced maps. second part, invertible maps Young sets, taking into account a classical compression technique along stable direction that allows reduction return map associated set to map. both c...

The paper proves transportation inequalities for probability measures on spheres the Wasserstein metrics with respect to cost functions that are powers of geodesic distance. Let $\mu$ be a measure sphere ${\bf S}^n$ form $d\mu =e^{-U(x)}{\rm d}x$ where ${\rm is rotation invariant measure, and $(n-1)I+{\hbox {Hess}}\,U\geq {\kappa _U}I$ , $\kappa _U>0$ . Then any $\nu$ finite relative entropy...

Recently, Verlinde noted a surprising similarity between Friedmann equation governing radiation dominated universe and Cardy’s entropy formula in conformal field theory. In this note, we study a brane-universe filled with radiation and stiff-matter. We analyze Friedmann equation in this context and compare our results with Cardy’s entropy formula.

We discuss the entropy of a circular polymer under a topological constraint. We call it the topological entropy of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula ...

Abstract—The problems of conditional entropy’s definition and the formula to compute conditional entropy are analyzed from various perspectives, and the corrected computing formula is presented. Examples are given to prove the conclusion that conditional entropy never be increased is not absolute, thus the representation that information is to decrease uncertainty in the definition of informati...