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What is Formal Concept

Chapter 18
Handbook of Research on Fuzzy Information Processing in Databases
A formal concept of a formal context (table) is a pair where and are collections (sets or fuzzy sets) of objects and attributes from and , respectively which satisfy that is the collection of all objects sharing all attributes from and is the collection of all attributes shared by all objects 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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Chapter 57
Mining Frequent Closed Itemsets for Association Rules
A formal context K = (G,M,I) consists of two sets G (objects) and M (attributes) and a relation I between G and M. For a set A?G of objects A’={meM | gIm for all geA} (the set of all attributes common to the objects in A). Correspondingly, for a set B of attributes we define B’ = {geG | gIm for all meB} (the set of objects common to the attributes in B). A formal concept of the context (G,M,I) is a pair (A,B) with A?G,B?M, such that A’=B and B’=A A is called the extent and B is the intent of the Formal Concept (A,B).
Published in Chapter: Mining Frequent Closed Itemsets for Association Rules; From: Handbook of Research on Innovations in Database Technologies and Applications: Current and Future Trends
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Chapter 12
Algorithms for Association Rule Mining
A formal context K = (G,M,I) consists of two sets G (objects) and M (attributes) and a relation I between G and M. For a set A?G of objects, A’={meM | gIm for all geA} (the set of all attributes common to the objects in A). Correspondingly, for a set B of attributes we define, B’ = {geG | gIm for all meB} (the set of objects common to the attributes in B). A formal concept of the context (G,M,I) is a pair (A,B) with A?G,B?M, A’=B and B’=A, A is called the extent and B is the intent of the concept (A,B).
Published in Chapter: Algorithms for Association Rule Mining; From: Encyclopedia of Artificial Intelligence
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