Rough Sets: From Rudiments to Challenges

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In the development of rough set theory and applications, one can distinguish three main stages. At the beginning, the researchers concentrated on descriptive properties such as reducts of information systems preserving indiscernibility relations or description of concepts or classifications. Next, they moved to applications of rough sets in machine learning, pattern recognition and data mining. After gaining some experiences, they developed foundations for inductive reasoning leading to, for example, inducing classifiers. While the first period was based on the assumption that objects are perceived by means of partial information represented by attributes, the second period was based on the assumption that information about the approximated concepts is partial too. Approximation spaces and searching strategies for relevant approximation spaces were recognized as the basic tools for rough sets. Important achievements both in theory and applications were obtained using Boolean reasoning and approximate Boolean reasoning applied, for example, in searching for relevant features, discretization, symbolic value grouping, or, in more general sense, in searching for relevant approximation spaces. Nowadays, we observe that a new period is emerging in which two new important topics are investigated: (i) strategies for discovering relevant (complex) contexts of analysed objects or granules, what is strongly related to information granulation process and granular computing, and (ii) interactive computations on granules. Both directions are aiming at developing tools for approximation of complex vague concepts, such as behavioural patterns or adaptive strategies, making it possible to achieve the satisfactory qualities of realized interactive computations. This chapter presents this development from rudiments of rough sets to challenges, for example, related to ontology approximation, process mining, context inducing or Perception-Based Computing (PBC). The approach is based on Interactive Rough-Granular Computing (IRGC).