Research on Uncertainty of Rough Fuzzy Sets in Different Knowledge Granularity Levels

The rough fuzzy sets (RFS) is a combination granular computing model with rough sets and fuzzy sets. Its uncertainty includes roughess, rough entropy, fuzziness and fuzzy entropy, etc.. In this paper, the changes of roughness, cut-set and fuzziness are discussed according to the knowledge granularity in different knowledge granularity levels in apporiximation spaces of rough fuzzy sets. Hence, the regularity of the uncertainty of rough fuzzy sets in different knowledge granularity levels is discovered, namely the roughness and fuzziness of rough fuzzy sets will decrease with the refinement of knowledge granularity in approximation spaces, and the cut-set of lower approximations will increase and the cut-set of upper approximations will decrease.