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Algebras of Definable Sets vs. Concept Lattices

Wasilewski Piotr

Fundamenta Informaticae

2019

Vol. 167, nr 3

235--256

The paper is aimed at comparing Rough Set Theory (RST) and Formal Concept Analysis (FCA) with respect to algebraic structures of concepts appearing in both theories, namely algebras of definable sets and concept lattices. The paper presents also basic ideas and concepts of RST and FCA together with some set theoretical concepts connected with set spaces which can serve as a convenient platform for a comparison of RST and FCA. In the last section there are shown necessary and sufficient conditions for the fact, that families of definable sets and concept extents determined by the same formal contexts are equal. This in finite cases is equivalent to an isomorphism of respective structures and generally reflects a very specific situation when both theories give the same conceptual hierarchies.

A comprehensive survey on formal concept analysis, its research trends and applications

Singh P. K., Aswani Kumar C., Gani A.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 2

495--516

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.