Density Peak Clustering (DPC) has attracted widespread attention in the recent decade. However, traditional DPC algorithms still have shortcomings such as difficulty in describing data distribution and sensitivity to parameters and allocation strategies. To address these shortcomings, this paper introduces an adaptive shared nearest neighbor density peak clustering algorithm based on fuzzy logic. Our algorithm makes use of the concepts of natural nearest neighbor and shared nearest neighbor, and provides an effective method for estimating neighbor distance and local density. The number K of nearest neighbors is selected adaptively based on the dataset itself. Instead of manually selecting cluster centers from a decision graph, our algorithm automatically determines them. In addition, based on the idea of fuzzy logic, non-central data points are divided into different types and assigned using different methods, which improves the robustness and accuracy of assigning non-cluster central data points. With both synthetic and real datasets in experiments, our algorithm is shown to be effectiveness when compared with recent DPC-based algorithms.