To capture the uncertainty of information or knowledge in information systems, various information granulations, also known as knowledge granulations, have been proposed. Recently, several axiomatic definitions of information granulation have been introduced. In this paper, we try to improve these axiomatic definitions and give a universal construction of information granulation by relating information granulations with a class of functions of multiple variables. We show that the improved axiomatic definition has some concrete information granulations in the literature as instances.

This paper describes application of information granulation theory, on the analysis of hydrocyclone perforamance. In this manner, using a combining of Self Organizing Map (SOM) and Neuro-Fuzzy Inference System (NFIS), crisp and fuzzy granules are obtained(briefly called SONFIS). Balancing of crisp granules and sub fuzzy granules, within non fuzzy information (initial granulation), is rendered in an open-close iteration. Using two criteria, "simplicity of rules "and "adaptive threoshold error level", stability of algorithm is guaranteed. Validation of the proposed method, on the data set of the hydrocyclone is rendered.

Outline: This paper describes application of rough set theory, on the analysis of hydrocyclone operation. In this manner, using Self Organizing Map (SOM) as preprocessing step, best crisp granules of data are obtained. Then, using a combining of SOM and rough set theory (RST)-called SORST-, the dominant rules on the information table, obtained from laboratory tests, are extracted. Based on these rules, an approximate estimation on decision attribute is fulfilled. Finally, a brief comparison of this method with the SOM-NFIS system (briefly SONFIS) is highlighted.