This study presents a new knowledge-based fuzzy clustering called semi-supervised collaborative fuzzy clustering (S\(^{2}\)CFC), which emphasizes aggregating diverse knowledge sources rather than using them in separate steps to revealing structures of data objects stored across multiple data sites while maintaining data sharing restrictions. The proposed method aggregates fuzzy logic, semi-supervised and collaborative learning simultaneously into a unified objective function for both horizontal and vertical data site distributions. This unified behavior strengthens the principles of existing data analysis and the growth of the concept of knowledge-based fuzzy clustering. Also, the proposed objective function benefits from cases such as (a) using a more appropriate and compatible criterion with fuzzy concepts in reconciliation between the structure obtained from the data site and knowledge induced from semi-supervised and collaborative learning, (b) learning collaboration intensity between data sites (c) ability to adjust the fuzziness rate of the structures (d) explicit solutions for constituent variables. The proposed method is also reinforced with a preprocessing phase to resolve inconsistencies between the reference data site structure and received structures from other data sites before engaging in the collaboration phase with a fuzzy similarity measure based on set theoric measure. The comprehensive experimental results clearly indicate the importance of aggregation instead of knowledge sequential learning. Our method outperforms in both horizontal and vertical modes its series of rival techniques in terms of accuracy, precision, recall, specificity, NMI, ARI, and convergence speed.

本研究提出了一种新的基于知识的模糊聚类，称为半监督协同模糊聚类 (S \(^{2}\)CFC)，它强调聚合不同的知识源，而不是在单独的步骤中使用它们来揭示跨多个数据站点存储的数据对象的结构，同时保持数据共享限制。所提出的方法将模糊逻辑、半监督和协作学习同时聚合成一个统一的目标函数，用于水平和垂直数据站点分布。这种统一行为加强了现有数据分析的原则和基于知识的模糊聚类概念的发展。此外，所提出的目标函数受益于以下情况，例如（a）在从数据站点获得的结构与从半监督和协作学习中获得的知识之间的协调中，使用带有模糊概念的更合适和兼容的标准，(b) 学习数据站点之间的协作强度 (c) 调整结构模糊率的能力 (d) 组成变量的显式解决方案。所提出的方法还通过预处理阶段得到加强，以解决参考数据站点结构与从其他数据站点接收的结构之间的不一致，然后再使用基于集合理论度量的模糊相似性度量进行协作阶段。综合实验结果清楚地表明聚合而不是知识顺序学习的重要性。我们的方法在水平和垂直模式下在准确性、精确度、召回率、特异性、NMI、ARI 和收敛速度方面都优于其一系列竞争技术。