Granular worlds: Representation and communication problems

In this study, we introduce a concept of granular worlds and elaborate on various representation and communication issues arising therein. A granular world embodies a collection of information granules being regarded as generic conceptual entities used to represent knowledge and handle problem solving. Granular computing is a paradigm supporting knowledge representation, coping with complexity, and facilitating interpretation of processing. In this sense, it is crucial to all man-machine pursuits and data mining and intelligent data analysis, in particular. There are two essential facets that are inherently associated with any granular world, that is a formalism used to describe and manipulate information granules and the granularity of the granules themselves (roughly speaking, by the granularity we mean a "size" of such information granules; its detailed definition depends upon the formal setting of the granular world). There are numerous formal models of granular worlds ranging from set-theoretic developments (including sets, fuzzy sets, and rough sets) to probabilistic counterparts (random sets, random variables and alike). In light of the evident diversity of granular world (occurring both in terms of the underlying formal settings as well as levels of granularity), we elaborate on their possible interaction and identify implications of such communication. More specifically, we have cast these in the form of the interoperability problem that is associated with the representation of information granules. © 2000 John Wiley & Sons, Inc.