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Concept approximations based on rough sets and similarity measures

100%
Saquer J., Deogun J. S.
International Journal of Applied Mathematics and Computer Science
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2001
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tom 11
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nr 3
655-674
EN
The formal concept analysis gives a mathematical definition of a formal concept. However, in many real-life applications, the problem under investigation cannot be described by formal concepts. Such concepts are called the non-definable concepts (Saquer and Deogun, 2000a). The process of finding formal concepts that best describe non-definable concepts is called the concept approximation. In this paper, we present two different approaches to the concept approximation. The first approach is based on rough set theory while the other is based on a similarity measure. We present algorithms for the two approaches.
2
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A comprehensive survey on formal concept analysis, its research trends and applications

88%
Singh P., Aswani Kumar C., Gani A.
International Journal of Applied Mathematics and Computer Science
|
2016
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tom 26
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nr 2
495-516
EN
In recent years, FCA has received significant attention from research communities of various fields. Further, the theory of FCA is being extended into different frontiers and augmented with other knowledge representation frameworks. In this backdrop, this paper aims to provide an understanding of the necessary mathematical background for each extension of FCA like FCA with granular computing, a fuzzy setting, interval-valued, possibility theory, triadic, factor concepts and handling incomplete data. Subsequently, the paper illustrates emerging trends for each extension with applications. To this end, we summarize more than 350 recent (published after 2011) research papers indexed in Google Scholar, IEEE Xplore, ScienceDirect, Scopus, SpringerLink, and a few authoritative fundamental papers.
3
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Unique factorization theorem for object-systems

88%
Mihók P., Semanišin G.
Discussiones Mathematicae Graph Theory
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2011
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tom 31
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nr 3
559-575
EN
The concept of an object-system is a common generalization of simple graph, digraph and hypergraph. In the theory of generalised colourings of graphs, the Unique Factorization Theorem (UFT) for additive induced-hereditary properties of graphs provides an analogy of the well-known Fundamental Theorem of Arithmetics. The purpose of this paper is to present UFT for object-systems. This result generalises known UFT for additive induced-hereditary and hereditary properties of graphs and digraphs. Formal Concept Analysis is applied in the proof.
4
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Knowledge discovery in data using formal concept analysis and random projections

75%
Aswani Kumar C.
International Journal of Applied Mathematics and Computer Science
|
2011
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tom 21
|
nr 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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