The increased demand of Web services and diverse characteristics of users have resulted in a plethora of applications that aim to provide personalized services based on the heterogeneous needs and preferences of users. With the aim to enhance and support the personalization process of Web applications, an innovative adaptation mechanism is proposed. The mechanism is based on a series of psychometric measures which capture the cognitive style of users and a Computational Intelligence technique embracing Artificial Neural Networks and Fuzzy Logic. The proposed mechanism decides on the adaptation effects of Web applications and provides a personalized user experience. The proposed method has been evaluated with a user study and provides interesting insights with respect to the effect of adaptation in terms of task accuracy, performance and satisfaction of users while interacting with an adapted and a non-adapted version of the same Web environment.