Fuzzy rule-based models (FRBMs) are sound constructs to describe complex systems. However, in reality, we may encounter situations, where the user or owner of a system only owns either the input or output data of that system (the other part could be owned by another user); and due to the consideration of data privacy, he/she could not obtain all the needed data to build the FRBMs. Since this type of situation has not been fully realized (noticed) and studied before, our objective is to come up with some strategy to address this challenge to meet the specific privacy consideration during the modeling process. In this study, the concept and algorithm of the collaborative fuzzy clustering (CFC) are applied to the identification of FRBMs, describing either multiple-input-single-output (MISO) or multiple-input-multiple-output (MIMO) systems. The collaboration between input and output spaces based on their structural information (conveyed in terms of the corresponding partition matrices) makes it possible to build FRBMs when input and output data could not be collected and used in unison. Surprisingly, on top of this primary pursuit, with the collaboration mechanism the input and output spaces of a system are endowed with an innovative way to comprehensively share, exchange, and utilize the structural information between each other, which results in their more relevant structures that guarantee better model performance compared with performance produced by some state-of-the-art modeling strategies. The effectiveness of the proposed approach is demonstrated by experiments on a series of synthetic and publicly available datasets.

中文翻译：

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使用协作模糊聚类识别基于模糊规则的模型。

基于模糊规则的模型 (FRBM) 是描述复杂系统的可靠结构。然而，在现实中，我们可能会遇到这样的情况，系统的用户或所有者只拥有该系统的输入或输出数据（另一部分可能由另一个用户拥有）；并且由于数据隐私的考虑，他/她无法获得构建 FRBM 所需的所有数据。由于这种情况之前尚未完全实现（注意到）和研究，因此我们的目标是提出一些策略来应对这一挑战，以满足建模过程中的特定隐私考虑。在这项研究中，协作模糊聚类 (CFC) 的概念和算法应用于 FRBM 的识别，描述了多输入单输出 (MISO) 或多输入多输出 (MIMO) 系统。输入和输出空间之间基于其结构信息的协作（根据相应的分区矩阵表示）使得在输入和输出数据无法统一收集和使用时构建 FRBM 成为可能。令人惊讶的是，在这个主要追求之上，通过协作机制，系统的输入和输出空间被赋予了一种创新的方式来全面共享、交换和利用彼此之间的结构信息，从而导致它们的结构更加相关，与一些最先进的建模策略产生的性能相比，保证更好的模型性能。通过对一系列合成和公开可用的数据集的实验证明了所提出方法的有效性。