Appendice : Note Sur l'ALGÈBRE Des Techniques d'ANALYSE Hiérarchique

Barbut, Marc

doi:10.1515/9783111540924-010

Cited by 5 publications

(4 citation statements)

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“…According to Barbut's result (Barbut, 1965) any lattice L can be represented as the Galois lattice of a bigraph (see Barbut and Monjardet, 1970).…”

Section: Remarkmentioning

confidence: 99%

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Some Order Dualities in Logic, Games and Choices

Monjardet

2007

Int. Game Theory Rev.

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We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally we present two "concrete" dualities occuring in social choice and in choice functions theories.

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“…According to Barbut's result (Barbut, 1965) any lattice L can be represented as the Galois lattice of a bigraph (see Barbut and Monjardet, 1970).…”

Section: Remarkmentioning

confidence: 99%

“…See for instance, Barbut andMonjardet, 1970, or Davey andPriestley, 1990. This duality between preorders and topologies plays important roles in many situations, for instance in the study of the structure of the (distributive) lattices of stable marriages (see Gusfield and Irving's book, 1989).…”

Section: ) In Early Work Of Tarski (For Instancementioning

confidence: 99%

Some Order Dualities in Logic, Games and Choices

Monjardet

2007

Int. Game Theory Rev.

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“…This chapter is concerned with formal concept analysis (FCA), which is a particular method of knowledge extraction from tabular data. Although some previous attempts exist, see (Barbut, 1965), FCA was initiated by Wille's seminal paper (Wille, 1982). Since then, significant progress has been made in theoretical foundations, algorithms, and methods.…”

Section: Introduction Tabular Data Formal Concept Analysis and Relamentioning

confidence: 99%

Relational Data,Formal Concept Analysis, and Graded Attributes

Bělohlávek

2008

Handbook of Research on Fuzzy Information Processing in Databases

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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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“…Over the last two decades, research has demonstrated how concept lattices formalize conceptual structures by coding any kind of duality, such as the duality between the intent and the extent of a concept. Application in data analysis using this duality for analysing questionnaire data was done by Barbut (1965) and Barbut and Monjardet (1970) in the domain of social sciences. The concept lattices also named`Galois lattices' was then promoted by Wille (1982) and Ganter and Wille (1999), and then extended as a discipline called`formal concept analysis'.…”

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confidence: 99%