Quality of experience (QoE) in multimedia traffic has been the focus of extensive research in the last decade. The estimation of the QoE provides valuable input in order to measure the user satisfaction of a particular service. QoE estimation is challenging as it tries to measure a subjective metric where the user experience depends on a number of factors that cannot simply be measured. In this work, we present a methodology and a system based on fuzzy expert system to estimate the impact of network conditions (QoS) on the QoE of video traffic. At first, we conducted subjective tests to correlate network QoS metrics with participants' perceived QoE of video traffic. Second, we propose a No Reference method based on fuzzy expert system to estimate the network impact on the video QoE. The membership functions of the proposed fuzzy system are derived from normalized probability distributions correlating the QoS metrics with QoE. We propose a simple methodology to build the fuzzy inference rules. We evaluated our system in two different sets of experiments. The estimated video quality showed high correlation with the subjective QoE obtained from the participants in a controlled test. We integrated our system as part of a monitoring tool in an industrial IPTV test bed and compared its output with standard Video Quality Monitoring (VQM). The evaluation results show that the proposed video quality estimation method based on fuzzy expert system can effectively measure the network impact on the QoE.