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1 2015

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Knowledge Reduction in Crisply Generated Fuzzy Concept Lattices

Li M.-Z., Wang G.-Y.

Fundamenta Informaticae

2015

Vol. 142, nr 1-4

307--335

Knowledge reduction is a basic issue in knowledge representation and data mining. Although various methods have been developed to reduce the size of classical formal contexts, the reduction of formal fuzzy contexts based on fuzzy lattices remains a difficult problem owing to its complicated derivation operators. To address this problem, this paper proposes a method of knowledge reduction by reducing attributes in a formal fuzzy context based on the crisply generated fuzzy concept lattice. Employing the proposed approach, attributes which are non-essential to the structure of the crisply generated fuzzy concept lattice are removed. Discernibility matrix and Boolean function are employed to compute the attribute reducts of the formal fuzzy contexts, by which all the attribute reducts of the formal fuzzy contexts are determined without changing the structure of the lattice. Further, all the attributes are classified into three types by their significance in constructing the crisply generated fuzzy concept lattice. The characteristics of these types of attributes are also analyzed. Finally, the proposed method is used to conduct knowledge reduction in the variable threshold concept lattices, which is a complement to the existing knowledge reduction methods.