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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基于协同模糊聚类的基于模糊规则的模型识别。

基于模糊规则的模型（FRBM）是描述复杂系统的合理构造。但是，实际上，我们可能会遇到这样的情况，即系统的用户或所有者仅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）。并且出于对数据隐私的考虑，他/她无法获得构建FRBM所需的所有数据。由于这种情况尚未得到充分的认识（注意）和之前的研究，因此我们的目标是提出一些策略来应对这一挑战，从而在建模过程中满足特定的隐私考虑。在这项研究中，将协作模糊聚类（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。基于输入和输出空间的结构信息（以相应的分区矩阵表示）之间的协作，使得当无法统一收集和使用输入和输出数据时，可以构建FRBM。出乎意料的是，在这一主要追求的基础上，借助协作机制，系统的输入和输出空间被赋予了一种创新的方式，可以在彼此之间全面共享，交换和利用结构信息，从而形成了更相关的结构，与某些最新建模策略产生的性能相比，它可以确保更好的模型性能。通过对一系列合成的和公开可用的数据集进行实验，证明了该方法的有效性。