Knowledge reduction in formal fuzzy contexts

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, we propose a general method of knowledge reduction by reducing attributes and objects in formal fuzzy contexts based on the variable threshold concept lattices. Employing the proposed approaches, we remove attributes and objects which are non-essential to the structure of a variable threshold concept lattice, i.e., with a given threshold level, the concept lattice constructed from a reduced formal context is made identical to that constructed from the original formal context. Discernibility matrices and Boolean functions are, respectively, employed to compute the attribute reducts and object reducts of the formal fuzzy contexts, by which all the attribute reducts and object reducts of the formal fuzzy contexts are determined without changing the structure of the lattice.

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