We introduce an incremental learning method for the optimal construction of rule-based granular systems from numerical data streams. The method is developed within a multiobjective optimization framework considering the specificity of information, model compactness, and variability and granular coverage of the data. We use $\alpha$-level sets over Gaussian membership functions to set model granularity and operate with hyperrectangular forms of granules in nonstationary environments. The resulting rule-based systems are formed in a formal and systematic fashion. They can be useful in time series modeling, dynamic system identification, predictive analytics, and adaptive control. Precise estimates and enclosures are given by linear piecewise and inclusion functions related to optimal granular mappings.

中文翻译：

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来自数据流的最优基于规则的粒度系统

我们引入了一种增量学习方法，用于从数值数据流中优化构建基于规则的粒度系统。该方法是在多目标优化框架内开发的，考虑到信息的特殊性、模型的紧凑性以及数据的可变性和粒度覆盖范围。我们在高斯隶属函数上使用 $\alpha$ 级集来设置模型粒度，并在非平稳环境中使用超矩形形式的颗粒进行操作。由此产生的基于规则的系统以正式和系统的方式形成。它们可用于时间序列建模、动态系统识别、预测分析和自适应控制。精确的估计和封闭由与最佳粒度映射相关的线性分段和包含函数给出。