Affiliation:
1. School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
Abstract
A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler–Lagrange equation.
Funder
Key Project of Natural Science Foundation of Educational Committee of Henan Province
Subject
General Physics and Astronomy
Reference39 articles.
1. A mathematical theory of communication;Shannon;Bell Syst. Tech. J.,1948
2. Gray, R.M. (2011). Entropy and Information Theory, Springer Science & Business Media.
3. New metric invariant of transitive dynamical systems and endomorphisms of lebesgue spaces;Kolmogorov;Dokl. Russ. Acad. Sci.,1958
4. Some research problems in uncertainty theory;Liu;J. Uncertain Syst.,2009
5. Maximum joint entropy and information-based collaboration of automated learning machines;Malakar;AIP Conference Proceedings 31st,2012