Effective Attribute Reduction Algorithm Based on Fuzzy Uncertainties Using Shared Neighborhood Granulation

As a very prominent research application of the theory of rough sets, attribute reduction technique has made significant strides in a lot of fields, including decision making, granular computing, etc. In particular, fuzzy attribute reduction approaches contribute greatly in the presence of uncertain data. However, most of fuzzy relations used in these approaches lack the discriminant ability to sample similarity, failing to identify the feature significance satisfactorily. In this article, a novel scheme using the shared neighborhood fuzzy uncertainties is proposed. Firstly, the concept of shared neighborhood is formulated, and then employed to establish the fuzzy similarity relation that effectively captures the sample similarity. Secondly, two fuzzy uncertainty measures named joint entropy and discrimination index based on shared neighborhood fuzzy relation are defined, which can quantify the feature's significance to the uncertainty characterization. Finally, two heuristic searching algorithms are designed to identify reducts aimed at minimizing the fuzzy uncertainties. Some comparative studies are investigated to examine the advantage of the designed reduction algorithms in classifier modeling. The reported analyses on public data sets verify that the designed algorithms outperform some representative and latest algorithms.