Abstract: Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.
Abstract: Neighborhood Rough Sets (NRS) has been proven to
be an efficient tool for heterogeneous attribute reduction. However,
most of researches are focused on dealing with complete and noiseless
data. Factually, most of the information systems are noisy, namely,
filled with incomplete data and inconsistent data. In this paper, we
introduce a generalized neighborhood rough sets model, called
VPTNRS, to deal with the problem of heterogeneous attribute
reduction in noisy system. We generalize classical NRS model with
tolerance neighborhood relation and the probabilistic theory.
Furthermore, we use the neighborhood dependency to evaluate the
significance of a subset of heterogeneous attributes and construct a
forward greedy algorithm for attribute reduction based on it.
Experimental results show that the model is efficient to deal with noisy
data.