Clustering technics, like k-means and its extended version, fuzzy c-means clustering (FCM) are useful tools for identifying typical behaviours based on various attitudes and responses to well-formulated questionnaires, such as among forensic populations. As more or less standard questionnaires for analyzing aggressive attitudes do exist in the literature, the application of these clustering methods seems to be rather straightforward. Especially, fuzzy clustering may lead to new recognitions, as human behaviour and communication are full of uncertainties, which often do not have a probabilistic nature. In this paper, the cluster analysis of a closed forensic (inmate) population will be presented. The goal of this study was by applying fuzzy c-means clustering to facilitate the wider possibilities of analysis of aggressive behaviour which is treated as a heterogeneous construct resulting in two main phenotypes, premeditated and impulsive aggression. Understanding motives of aggression helps reconstruct possible events, sequences of events and scenarios related to a certain crime, and ultimately, to prevent further crimes from happening.

In this study, the entropy weight method, the α convergence model, the absolute β convergence model and the conditional β convergence model are used to evaluate the 31 provinces’ innovative potential in China from 2011 to 2022. It is found that the innovative potential in nationwide China and in various regions are all increasing year by year, and the innovative potential in the eastern region is obviously better than that in the central region and western region. No matter considering the influence of external factors or not, the gap of innovative potential among provinces in different regions will gradually expand over time, with the largest gap among provinces in the eastern region, followed by the central region and the smallest in the western region. The conclusion of this study is instructive to enhance the innovative potential of China and promote the balanced development of regional innovative potential in China.