In the theory of fuzzy measures, Choquet integral is one of the most important tools. The calculation of Choquet integral on real line is difficult for many cases such as nonmonotone functions. In this paper, by the geometric interpretation of Choquet integral, we introduce a new Choquet-like integral with a different algebraic interpretation of Choquet integral on real line. The calculation of this integral is simpler than Choquet integral on real line. Based on this integral, we introduce a general class of normal distribution on monotone measures. Finally, as an application, the real dataset obtained from the daily price of Dow Jones Industrial Average Index in period of June 2, 2008 to June 2, 2018 is analyzed.

中文翻译：

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一种新的非线性类 Choquet 积分，在基于单调测度的正态分布中的应用

在模糊测度理论中，Choquet 积分是最重要的工具之一。对于非单调函数等许多情况，实线上的 Choquet 积分的计算是困难的。在本文中，通过 Choquet 积分的几何解释，我们引入了一种新的 Choquet-like 积分，它具有对实线上 Choquet 积分的不同代数解释。该积分的计算比实线上的 Choquet 积分简单。基于这个积分，我们介绍了单调测度上的一般正态分布类。最后，作为应用，分析了从2008年6月2日至2018年6月2日期间道琼斯工业平均指数的每日价格获得的真实数据集。