Learning and prediction in a data streaming environment is challenging due to continuous arrival of enormous data in high speed that often evolves with time. In this paper we present a dynamically evolving fuzzy rule-based model that predicts and learns from each instance in the stream, taking into account the principal issues of streaming environment viz., limited memory, real time, and dynamic nature. The fuzzy model essentially uses a newly proposed dynamically evolving clustering method for learning the structure. Unlike other approaches that consider either the data density or distance from existing cluster centres, this approach considers both density and distance to decide if a new cluster is to be generated. To capture the dynamics of the data stream, the density is defined in both data and time space in such a way that it decays exponentially with time. A distinction is made between core and non-core clusters to effectively identify the real outliers. The experimental results using benchmark and real datasets show that the proposed approach attains results at par or better than existing approaches and significantly reduces the computational overhead.