Granular Computing, Computer Security andWeb Intelligence

What is granular computing? As we have said in [6]: There are no mathematically valid formal definitions yet. Informally, any computing theory/technology that involves elements and granules (generalized subsets) may be called granular computing (GrC). Intuitively, elements are the data, and granules are the basic knowledge. So granular computing includes data and knowledge computing/engineering, data mining, knowledge discovery, learning and the uncertainty management (granules of no knowledge). We may lump these subfields into AI-Engineering. Here granules will be interpreted as generalized subsets that include classical subsets, fuzzy subsets, and sets with neighborhood systems (e.g., the α cut as neighborhood systems of the cores). As fuzzy sets are defined by membership functions which are bounded real-valued functions, so we will extend further to all functions, even to generalized functions (e.g. Dirac functions), measures/probabilities, generalized measures (e.g. belief functions). In this paper, we will explain two killer applications.