| Granular computing is an emerging field of research that attempts to formalize and explore methods and heuristics for human problem solving with multiple levels of granularity and abstraction. A fundamental issue of granular computing is the construction, representation and utilization of granules and granular structures. Basic granules represent the basic pieces of knowledge. A granular structure reflects the connections between different pieces of knowledge. The main objective of this thesis is to examine a logic approach to address this issue. Following the classical interpretation where a concept consists of a pair containing an extension and an intension, we interpret a granule as a pair containing a set of objects and a logic formula describing the granule. The building blocks of granular structures are basic granules representing elementary concepts or pieces of knowledge. They are treated as atomic formulas of a logic language. Different types of granular structures can be constructed by using logic connectives. Within this logic framework, we show that rough set analysis (RSA) and formal concept analysis (FCA) can be interpreted uniformly by using the proposed logic language. The two theories share high-level similarities, but differ in their choices of definable granules and granular structures. Algorithms and evaluation measures can be designed uniformly for both theories. |
