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Information entropy and its extended forms have been widely used in various rough sets to evaluate the uncertainty of a fuzzy relation or a fuzzy granularity. However, they are difficult to estimate the distinguishing information of feature subsets derived from multisource data. On the one hand, most of them only have a single granulation and cannot characterize and fuse the distinguishing information from multiple granularity levels. On the other hand, they generally lack the ability to resist noise. When the data is mingled with noise, the classification performance will be greatly affected. To overcome these problems, this article put forth some novel distinguishing indicators for fuzzy covering (FBC) decision systems. First, we discussed the granulation structure of FBC and introduced a new multigranulation distinguishing indicator. Second, some variants of the distinguishing indicator, i. e. , multigranulation variable-precision conditional distinguishing indicator, multigranulation variable-precision joint distinguishing indicator, and multigranulation variable-precision mutual distinguishing indicator, are proposed to dynamically reflect the change of distinguishing information with respect to a given granulation structure. Finally, knowledge reduction is processed by the view of keeping the classification capacity, and a forward algorithm for feature subset selection with an optimistic variable-precision conditional distinguishing indicator is developed. Two kinds of numerical experiments are conducted on 12 benchmark datasets to examine the robustness and classification performance of the presented algorithm. Experimental results indicate that our method attains competitive classification performance compared with four popular dimensionality reduction algorithms and exhibits strong robustness when facing data noise.
Huang et al. (Wed,) studied this question.