Formal context is a triplet where and are finite sets of objects and attributes, respectively, and is a relation or fuzzy relation between and . A formal context can be represented by a table with rows and columns corresponding to objects and attributes, and table entries containing to degrees to which objects have attributes. In particular, if is an ordinary relation, table entries can contain only degrees and .
Published in Chapter:
Relational Data,Formal Concept Analysis, and Graded Attributes
Radim Belohlavek (Binghamton University – SUNY, USA and Palacky University, Czech Republic)
Copyright: © 2008
|Pages: 28
DOI: 10.4018/978-1-59904-853-6.ch018
Abstract
Formal concept analysis is a particular method of analysis of relational data. Also, formal concept analysis provides elaborate mathematical foundations for relational data. In the course of the last decade, several attempts appeared to extend formal concept analysis to data with graded (fuzzy) attributes. Among these attempts, an approach based on residuated implications plays an important role. This chapter presents an overview of foundations of formal concept analysis of data with graded attributes, with focus on the approach based on residuated implications and on its extensions and particular cases. Presented is an overview of both of the main parts of formal concept analysis, namely, concept lattices and attribute implications, and an overview of the underlying foundations and related methods. In addition to that, the chapter contains an overview of topics for future research.