A granular signature of data

In this paper, we discuss an issue of description of highly dimensional data realized in terms of fuzzy sets. The underlying idea is to granulate numeric data using fuzzy sets and afterwards reveal and quantify relationships between these granules. This naturally impacts the dimensionality of any original dataset under discussion and provides with its nonlinear transformation (through the corresponding membership functions). These information granules give rise to the notion of associations-multidimensional information granules. Being fuzzy relations, these constructs are direction free. The directionality arises when one defines inputs and outputs and in this way confines himself to some sort of rules capturing a directional nature of main relationships within the data. Rules arising from associations may be in conflict. The essence of data is then captured via a granular signature regarded as a mixture of associations and rules.