Knowledge Granulation, Rough Entropy and Uncertainty Measure in Incomplete Fuzzy Information System

Many real world problems deal with ordering of objects instead of classifying objects, although most of research in data analysis has been focused on the latter. One of the extensions of classical rough sets to take into account the ordering properties is dominance-based rough sets approach which is mainly based on substitution of the indiscernibility relation by a dominance relation. In this paper, we address knowledge measures and reduction in incomplete fuzzy information system using the approach. Firstly, new definitions of knowledge granulation and rough entropy are given, and some important properties of them are investigated. Then, dominance matrix about the measures knowledge granulation and rough entropy is obtained, which could be used to eliminate the redundant attributes in incomplete fuzzy information system. Lastly, a matrix algorithm for knowledge reduction is proposed. An example illustrates the validity of this method and shows the method is applicable to complex fuzzy system. Experiments are also made to show the performance of the newly proposed algorithm.