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Knowledge Reduction in Crisply Generated Fuzzy Concept Lattices

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

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

307--335

EN

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.

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Knowledge discovery in data using formal concept analysis and random projections

Aswani Kumar Ch.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 4

745-756

EN

In this paper our objective is to propose a random projections based formal concept analysis for knowledge discovery in data. We demonstrate the implementation of the proposed method on two real world healthcare datasets. Formal Concept Analysis (FCA) is a mathematical framework that offers a conceptual knowledge representation through hierarchical conceptual structures called concept lattices. However, during the design of a concept lattice, complexity plays a major role.

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Relational Contexts and Relational Concepts

Jiang F., Sui Y., Cao C.

Fundamenta Informaticae

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2010

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Vol. 99, nr 3

293-314

EN

Formal concept analysis (FCA) is a mathematical description and theory of concepts implied in formal contexts. And the current formal contexts of FCA aim to model the binary relations between individuals (objects) and attributes in the real world. In the real world we usually describe each individual by some attributes, which induces the relations between individuals and attributes. But there also exist many relations between individuals, for instance, the parent-children relation in a family. In this paper, to model the relations between individuals in the real world, we propose a new context - relational context for FCA, which contains a set U of objects and a binary relation r on U. Corresponding to the formal concepts in formal contexts, we present different kinds of relational concepts in relational contexts, which are the pairs of sets of objects. First we define the standard relational concepts in relational contexts. Moreover, we discuss the indirect relational concepts and negative relational concepts in relational contexts, which aim to concern the indirection and negativity of the relations in relational contexts, respectively. Finally, we define the hybrid relational concepts in relational contexts, which are the combinations of any two different kinds of relational concepts. In addition, we also discuss the application of relational contexts and relational concepts in the supply chain management field.