Rough-fuzzy image analysis: Granular mining

摘要

The role of rough sets in uncertainty handling and granular computing is described. The relevance of its integration with fuzzy sets, namely, rough-fuzzy computing, as a stronger paradigm for uncertainty handling, is explained. Different applications of rough granules, significance of f-granulation and other important issues in their implementations are stated. Generalized rough sets using fuzziness in granules as well as in sets are defined both for equivalence and tolerance relations. These are followed by different rough-fuzzy entropy definitions. As an example of fuzzy granular computing and granular fuzzy computing tasks like case generation, class-dependent granulation for classification, and measuring image ambiguity measures for segmentation and mining are then addressed, explaining the nature, role and characteristics of granules used therein.