Feature space theory in data mining: transformations between extensions and intensions in knowledge representation

Knowledge representation is one of the important topics in data mining research. In this paper, based on the feature space theory in data mining, the transformation between extensions and intensions of concepts is discussed in detail. First, inner projections of fuzzy relations, as a basic mathematical tool, are defined, and properties of inner projections are discussed. Then inner transformation of fuzzy relations, inverse inner transformations, and related properties are introduced The concept structure is shown by feature spaces. Lastly, transformations between extensions and intensions are discussed.