Enhancing the ability to make informed decisions stands as a significant challenge in modern IT. Specifically, there is a growing need to improve the efficiency of classification algorithms. When faced with multiple results derived from various methods, one can select the most probable decision using a robust aggregation operator. A common class of algorithms employed for this purpose is based on extensions of the Choquet integral (CI). In this study, we introduce and extensively analyze a novel aggregation operator concept founded on the generalization of the CI. This approach leverages quadrature formulae to calculate Choquet integral values, but with a unique modification involving a smoothing operation. This refinement results in more precise values, preserving the essential characteristics of the Choquet integral. These refined values can be effectively applied in the aggregation of classifiers and, more broadly, in information fusion processes. A series of numerical experiments demonstrates the efficiency of our approach. Furthermore, we thoroughly discuss and provide mathematical proofs for the properties of the newly constructed operators.

中文翻译：

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光滑和增强光滑求积广义 Choquet 积分的分析

提高做出明智决策的能力是现代 IT 领域的一项重大挑战。具体来说，提高分类算法效率的需求日益增长。当面对从各种方法得出的多个结果时，可以使用稳健的聚合算子选择最可能的决策。为此目的采用的一类常见算法基于 Choquet 积分 (CI) 的扩展。在本研究中，我们介绍并广泛分析了一种基于 CI 泛化的新颖聚合算子概念。该方法利用求积公式来计算 Choquet 积分值，但进行了涉及平滑操作的独特修改。这种细化会产生更精确的值，保留 Choquet 积分的基本特征。这些精炼值可以有效地应用于分类器的聚合，更广泛地应用于信息融合过程。一系列数值实验证明了我们方法的效率。此外，我们对新构造的算子的性质进行了深入的讨论并提供了数学证明。