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What is Attribute Implication

Chapter 18
Handbook of Research on Fuzzy Information Processing in Databases
An attribute implication is an expression such that and are collections (sets of fuzzy sets) of attributes. The basic meaning of being true in a formal context (table) is: every object from which has all attributes from has also all attributes from .
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.
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