Granular computing and knowledge reduction are two basic issues in knowledge representation and data mining. Granular structure of concept lattices with application in knowledge reduction in formal concept analysis is examined in this paper. Information granules and their properties in a formal context are first discussed. Concepts of a granular consistent set and a granular reduct in the formal context are then introduced. Discernibility matrices and Boolean functions are, respectively, employed to determine granular consistent sets and calculate granular reducts in formal contexts. Methods of knowledge reduction in a consistent formal decision context are also explored. Finally, knowledge hidden in such a context is unraveled in the form of compact implication rules.

This paper proposes a novel rough set approach to discover classification rules in real‐valued spatial data in general and remotely sensed data in particular. A knowledge induction process is formulated to select optimal decision rules with a minimal set of features necessary and sufficient for a remote sensing classification task. The approach first converts a real‐valued or integer‐valued decision system into an interval‐valued information system. A knowledge induction procedure is then formulated to discover all classification rules hidden in the information system. Two real‐life applications are made to verify and substantiate the conceptual arguments. It demonstrates that the proposed approach can effectively discover in remotely sensed data the optimal spectral bands and optimal rule set for a classification task. It is also capable of unraveling critical spectral band(s) discerning certain classes. The framework paves the road for data mining in mixed spatial databases consisting of qualitative and quantitative data.

This article deals with approaches to knowledge reductions in inconsistent information systems (ISs). The main objective of this work was to introduce a new kind of knowledge reduction called a maximum distribution reduct, which preserves all maximum decision classes. This type of reduction eliminates the harsh requirements of the distribution reduct and overcomes the drawback of the possible reduct that the derived decision rules may be incompatible with the ones derived from the original system. Then, the relationships among the maximum distribution reduct, the distribution reduct, and the possible reduct were discussed. The judgement theorems and discernibility matrices associated with the three reductions were examined, from which we can obtain approaches to knowledge reductions in rough set theory (RST). © 2003 Wiley Periodicals, Inc.