With the proliferation of web services on the Inter-net, it has become important for service providers to select the best services for their clients in accordance to their functional and non-functional requirements. Generally, QoS parameters are used to select the most performing web services, however, these parameters do not necessarily reflect the user's satisfaction. Therefore, it is necessary to estimate the quality of web services on the basis of user satisfaction, i.e., Quality of Experience(QoE). In this paper, we propose a novel method based on a fuzzy-rough hybrid expert system for estimating QoE of web services for web service selection. It also presents how different QoS parameters impact the QoE of web services. For this, we conducted subjective tests in controlled environment with real users to correlate QoS parameters to subjective QoE. Based on this subjective test, we derive membership functions and inference rules for the fuzzy system. Membership functions are derived using a probabilistic approach and inference rules are generated using Rough Set Theory (RST). We evaluated our system in a simulated environment in MATLAB. The simulation results show that the estimated web quality from our system has a high correlation with the subjective QoE obtained from the participants in controlled tests