Fundamental properties of relative entropy and Lin divergence for Choquet integral

摘要

Entropy is the most important concept used in information theory and measuring uncertainty. In Choquet calculus, Sugeno (2013) [10] and Torra and Narukawa (2016) [2] studied Choquet integral and derivative with respect to monotone measures on the real line. Then as a very challenging problem, the definition of entropy and relative entropy on monotone measures for infinite sets based on Choquet integral was proposed by Torra (2017) [1] and Agahi (2019) [12]. These results show that based on the submodularity condition on monotone measures, entropy and relative entropy for Choquet integral are non-negative.In this paper, we first introduce the concept of Lin divergence (Lin, 1991, [8]), including Choquet integral and derivative with respect to monotone measures. Then some fundamental properties of this concept in information theory are given. In special case, we show that we can omit the submodularity condition in previous results on entropy and relative entropy for Choquet integral. (C) 2021 Published by Elsevier Inc.