Attribute reduction is one of the biggest challenges encountered in computational intelligence, data mining, pattern recognition and machine learning. Effective in feature selection as the rough set theory is, it can only handle symbolic attributes. In order to overcome this drawback, proposed is the fuzzy rough sets, an extended model of rough sets, which is able to deal with imprecision and uncertainty in both symbolic and numerical attributes. Existing attribute selection algorithms based on fuzzy rough set model mainly take the angle of “attribute set”, which means they define the object function representing the predictive ability for attributes subset with regard to the domain of discourse, rather than follow the view of “object pair”. Algorithms based on the latter can ignore the object pairs that are already discerned by the selected attributes subsets and thus need only to deal with part of object pairs instead of the whole object pairs from the discourse, which makes such algorithms more efficient in attribute selection. In this paper, we propose the concept of Reduced Maximal Discernibility Pair, which directly adopts the perspective of object pair in the framework of fuzzy rough set model. Then we develop two attribute selection algorithms, named as Reduced Maximal Discernibility Pair Selection (RMDPS) and Weighted Reduced Maximal Discernibility Pair Selection (WRMDPS), based on the reduced maximal discernibility pair. Experiment results show that the proposed algorithms are effective and efficient in attribute selection.

Uncertainty measures can supply new viewpoints for analyzing data. They can help us in disclosing the substantive characteristics of data. The uncertainty measurement issue is also a key topic in the rough-set theory. Although there are some measures to evaluate the uncertainty for complete decision systems (also called decision tables), they cannot be trivially transplanted into incomplete decision systems. There are relatively few studies on uncertainty measurement in incomplete decision systems. In this paper, we propose a new form of conditional entropy, which can be used to measure the uncertainty in incomplete decision systems. Some important properties of the conditional entropy are obtained. In particular, two validity theorems guarantee that the proposed conditional entropy can be used as a reasonable uncertainty measure for incomplete decision systems. Experiments on some real-life data sets are conducted to test and verify the validity of the proposed measure. Applications of the proposed uncertainty measure in ranking attributes and feature selection are also studied with experiments.

Attribute selection is considered as the most characteristic result in rough set theory to distinguish itself to other theories. However, existing attribute selection approaches can not handle partially labeled data. So far, few studies on attribute selection in partially labeled data have been conducted. In this paper, the concept of discernibility pair based on rough set theory is raised to construct a uniform measure for the attributes in both supervised framework and unsupervised framework. Based on discernibility pair, two kinds of semisupervised attribute selection algorithm based on rough set theory are developed to handle partially labeled categorical data. Experiments demonstrate the effectiveness of the proposed attribute selection algorithms.