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A Formal Framework and New Related Methods when Fancing with Granularity in Unsupervised Learning

Classical data mining methods are currently involved in the descriptive forming of information granules. However, this is the first level of abstraction. Afterwards, we are facing with a new challenge: processing information granules and organizing them into more complex cognitive structures. There are several formal frameworks in which information granules are built, captured or processed: Fuzzy sets, Rough sets, Shadowed sets, Modal sets, Interval mathematics and so on. This paper is intended to consider multidimensional fuzzy granules as primary events (genuine outcomes of a set of fuzzyvalued random variables) and to address a second level of abstraction by using knowledge discovery methods based on the granular computing paradigm.