Abstract
•We discuss a way of building, refining, and generalizing information granules.•Refinement of information granules is realized by assessing their information content.•General optimization procedure of successive refinement of information granules is provided.•Conditional Fuzzy C-Means is discussed as an efficient vehicle to realize information granulation.•Discussed are granular decision trees as generic models with information granules.
This study is concerned with a fundamental problem of expanding (refining) information granules being treated as functional entities playing a pivotal role in Granular Computing and ensuing constructs such as granular models, granular classifiers, and granular predictors. We formulate a problem of refinement of information granules as a certain optimization task in which a selected information granule is refined into a family of more detailed (precise, viz. more specific) information granules so that a general partition requirement becomes satisfied. As the ensuing information granules are directly linked with the more general information granule positioned at the higher level of hierarchy, the partition criterion is conditional by being implied (conditioned) by the description of the granule positioned one level up in the hierarchy. A criterion guiding a refinement of information granules is formulated and made fully reflective of the nature of the problem (being of regression-like or of classification character), which leads to a distinct way in which the diversity of information granules is articulated and quantified. With regard to the detailed algorithmic setting, we discuss the use of a so-called conditional Fuzzy C-Means and show how information granules (fuzzy sets) are formed in a successive manner. The method helps highlight the ensuing calculations of the resulting membership functions and reveal how the detailed structure of the data is captured. A number of numeric studies in the realm of system modeling are provided to demonstrate the performance of the approach and highlight the nature of the resulting information granules along with the performance of the fuzzy models in which these information granules are used.