The Hypertext Transfer Protocol (HTTP) Adaptive Streaming (HAS) has now become ubiquitous and accounts for a large amount of video delivery over the Internet. But since the Internet is prone to bandwidth variations, HAS's up and down switching between different video bitrates to keep up with bandwidth variations leads to a reduction in Quality of Experience (QoE). In this article, we propose a video bitrate adaptation and prediction mechanism based on Fuzzy logic for HAS players, which takes into consideration the estimate of available network bandwidth as well as the predicted buffer occupancy level in order to proactively and intelligently respond to current conditions. This leads to two contributions: First, it allows HAS players to take appropriate actions, sooner than existing methods, to prevent playback interruptions caused by buffer underrun, reducing the ON-OFF traffic phenomena associated with current approaches and increasing the QoE. Second, it facilitates fair sharing of bandwidth among competing players at the bottleneck link. We present the implementation of our proposed mechanism and provide both empirical/QoE analysis and performance comparison with existing work. Our results show that, compared to existing systems, our system has (1) better fairness among multiple competing players by almost 50% on average and as much as 80% as indicated by Jain's fairness index and (2) better perceived quality of video by almost 8% on average and as much as 17%, according to the estimate the Mean Opinion Score (eMOS) model.