Fuzzy models have been commonly used in system modeling and model-based control. Among various fuzzy models, Takagi–Sugeno (TS) fuzzy models form one of the intensively studied and applied categories of models. In this study, we are concerned with a development of a granular TS fuzzy model realized on a basis of numerical evidence and completed through a combination of fuzzy subspace clustering and the principle of optimal allocation of information granularity. The TS fuzzy models are built with the use of the fuzzy subspace clustering algorithm. Information granularity is regarded as a crucial design asset whose optimal allocation gives rise to granular fuzzy models and makes the constructed models to become better in rapport with experimental data. In comparison with fuzzy models, granular fuzzy models produce results (outputs) that are information granules rather than numeric entities being encountered in fuzzy models. In contrast with the commonly used optimization criteria, which emphasize the highest accuracy encountered at the numeric level, the performance of the granular TS fuzzy model is quantified in terms of the coverage and specificity criteria where such criteria are of interest in the evaluation of quality of information granules vis-à-vis experimental (numeric) data. Experimental results are reported for both synthetic datasets and publicly available data sets coming from the UCI machine learning repository.

中文翻译：

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通过模糊子空间聚类和信息粒度优化分配的协同设计粒状Takagi-Sugeno模糊模型

模糊模型已普遍用于系统建模和基于模型的控制。在各种模糊模型中，Takagi-Sugeno (TS) 模糊模型形成了深入研究和应用的模型类别之一。在本研究中，我们关注的是基于数值证据实现的粒度 TS 模糊模型的开发，并通过模糊子空间聚类和信息粒度优化分配原则的组合完成。TS 模糊模型是使用模糊子空间聚类算法建立的。信息粒度被认为是一种关键的设计资产，它的优化分配产生了粒度模糊模型，并使构建的模型与实验数据更好地吻合。与模糊模型相比，颗粒模糊模型产生的结果（输出）是信息颗粒，而不是模糊模型中遇到的数字实体。与强调在数值级别遇到的最高准确度的常用优化标准相比，粒度 TS 模糊模型的性能根据覆盖率和特异性标准进行量化，其中这些标准对评估质量相对于实验（数字）数据的信息颗粒。报告了合成数据集和来自 UCI 机器学习存储库的公开可用数据集的实验结果。粒度 TS 模糊模型的性能根据覆盖率和特异性标准进行量化，其中这些标准在评估信息颗粒相对于实验（数字）数据的质量时很重要。报告了合成数据集和来自 UCI 机器学习存储库的公开可用数据集的实验结果。粒度 TS 模糊模型的性能根据覆盖率和特异性标准进行量化，其中这些标准在评估信息颗粒相对于实验（数字）数据的质量时很重要。报告了合成数据集和来自 UCI 机器学习存储库的公开可用数据集的实验结果。