Rough Sets: Trends and Challenges

We discuss how approximation spaces considered in the context of rough sets and information granule theory have evolved over the last 20 years from simple approximation spaces to more complex spaces. Some research trends and challenges for the rough set approach are outlined in this paper. The study of the evolution of approximation space theory and applications is considered in the context of rough sets introduced by Zdzisław Pawlak and the notions of information granulation and computing with words formulated by Lotfi Zadeh. The deepening of our understanding of information granulation and the introduction to new approaches to concept approximation, pattern identification, pattern recognition, pattern languages, clustering, information granule systems, and inductive reasoning have been aided by the introduction of a calculus of information granules based on rough mereology. Central to rough mereology is the inclusion relation to be a part to a degree. This calculus has grown out of an extension of what S. Leśniewski called mereology (the study of what it means to be a part of).