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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.

A Comparative Study of Algebra Viewpoint and Information Viewpoint in Attribute Reduction

Wang G.-Y., Zhao J., An J., Wu Y.

Fundamenta Informaticae

2005

Vol. 68, nr 3

289--301

Attribute reduction is an important issue in rough set theory and has already been studied from the algebra viewpoint and information viewpoint of rough set theory respectively. However, the concepts of attribute reduction based on these two different viewpoints are not equivalent to each other. In this paper, we make a comparative study on the quantitative relationship between some basic concepts of rough set theory like attribute reduction, attribute significance and core defined from these two viewpoints. The results show that the relationship between these conceptions from the two viewpoints is rather an inclusion than an equivalence due to the fact that the rough set theory discussed from the information point of view restricts attributes and decision tables more specifically than it does when considered from the algebra point of view. The identity of the two viewpoints will hold in consistent information decision tables only. That is, the algebra viewpoint and information viewpoint are equivalent for a consistent decision table, while different for an inconsistent decision table. The results are significant for the design and development of methods for information reduction.