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.

熵是信息论和测量不确定性中最重要的概念。在Choquet演算中，Sugeno（2013）[10]和Torra and Narukawa（2016）[2]研究了Choquet积分和导数与实线上单调测度的关系。然后，作为一个非常具有挑战性的问题，Torra（2017）[1]和Agahi（2019）[12]提出了基于Choquet积分的无穷集单调测度的熵和相对熵的定义。这些结果表明，基于单调测度的亚模条件，Choquet积分的熵和相对熵为非负。

在本文中，我们首先介绍Lin散度的概念（Lin，1991，[8]），包括关于单调测度的Choquet积分和导数。然后给出了该概念在信息论中的一些基本性质。在特殊情况下，我们证明了我们可以忽略先前关于Choquet积分的熵和相对熵的亚模条件。