By introducing a novel attribute reduction algorithm based on an extension neighborhood relation, it defeated the decision problem of the complete mixed system in classical rough sets theory. The proposed algorithm could also treat the incomplete mixed decision system, which missed some attribute values in complete mixed attribute data sets. The neighborhood threshold and the variable precision threshold were employed in the extension neighborhood relation as the restrictions to select positive region of decision, and the significance of attributes in this positive region was taken as the heuristic factor. The outstanding property of the proposed algorithm was to handle the nominal attributes, the numerical attributes and the missing attributes simultaneously without discretizing the numerical attributes or completing the incomplete data. The proposed algorithm was tested on the UCI data sets, and the experiment results showed that it could select the core attributes still keeping or even improving classification accuracy. Also it was discussed that how to influence the classification when specifying the values of the two mentioned threshold parameters used in the extension neighborhood relation. © 2013 Binary Information Press.
