Applying domain knowledge in fuzzy clustering algorithms continuously promotes the development of clustering technology. The combination of domain knowledge and fuzzy clustering algorithms has some problems, such as initialization sensitivity and information granule weight optimization. Therefore, we propose a weighted kernel fuzzy clustering algorithm based on a relative density view (RDVWKFC). Compared with the traditional density-based methods, RDVWKFC can capture the intrinsic structure of the data more accurately, thus improving the initial quality of the clustering. By introducing a Relative Density based Knowledge Extraction Method (RDKM) and adaptive weight optimization mechanism, we effectively solve the limitations of view initialization and information granule weight optimization. RDKM can accurately identify high-density regions and optimize the initialization process. The adaptive weight mechanism can reduce noise and outliers’ interference in the initial cluster centre selection by dynamically allocating weights. Experimental results on 14 benchmark datasets show that the proposed algorithm is superior to the existing algorithms in terms of clustering accuracy, stability, and convergence speed. It shows adaptability and robustness, especially when dealing with different data distributions and noise interference. Moreover, RDVWKFC can also show significant advantages when dealing with data with complex structures and high-dimensional features. These advancements provide versatile tools for real-world applications such as bioinformatics, image segmentation, and anomaly detection.

The research on complex systems is different from that on general systems because the former must consider self-organization, emergence, uncertainty, predetermination, and evolution. As an important method to transform the world, a simulation is one of the most important skills to discover complex systems. In this study, we provide a survey on complex systems and their simulation methods. Initially, the development history of complex system research is summarized from two main lines. Then, the eight common characteristics of the most complex systems are presented. Furthermore, the simulation methods of complex systems are introduced in detail from four aspects, namely, meta-synthesis methods, complex networks, intelligent technologies, and other methods. From the overall point of view, intelligent technologies are the driving force, and complex networks are the advanced structure. Meta-synthesis methods are the integration strategy, and other methods are the supplements. In addition, we show three complex system simulation examples: digital reactor simulation, simulation of a logistics system in the industrial site, and crowd evacuation simulation. The examples show that a simulation is a useful means and an important method in complex system research. Finally, the future development prospects for complex systems and their simulation methods are suggested.