The fuzzy integral is a powerful parametric nonlin-ear function with utility in a wide range of applications, from information fusion to classification, regression, decision making,interpolation, metrics, morphology, and beyond. While the fuzzy integral is in general a nonlinear operator, herein we show that it can be represented by a set of contextual linear order statistics(LOS). These operators can be obtained via sampling the fuzzy measure and clustering is used to produce a partitioning of the underlying space of linear convex sums. Benefits of our approach include scalability, improved integral/measure acquisition, generalizability, and explainable/interpretable models. Our methods are both demonstrated on controlled synthetic experiments, and also analyzed and validated with real-world benchmark data sets.

中文翻译：

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模糊积分 = 上下文线性顺序统计

模糊积分是一种强大的参数非线性函数，具有广泛的应用，从信息融合到分类、回归、决策、插值、度量、形态学等。虽然模糊积分通常是一个非线性算子，但在这里我们表明它可以用一组上下文线性顺序统计（LOS）来表示。这些算子可以通过对模糊测度进行抽样获得，并且聚类用于产生线性凸和的基础空间的划分。我们方法的好处包括可扩展性、改进的积分/测量获取、通用性和可解释/可解释的模型。我们的方法既在受控合成实验中得到证明，也用真实世界的基准数据集进行分析和验证。