We present a unique framework for connecting different topics: hypergraphs from one side and Formal Concept Analysis and Rough Set Theory from the other. This is done through the formal equivalence among Boolean information tables, formal contexts and hypergraphs. Links with generic (i.e., not Boolean) information tables are established, through so-called nominal scaling. The particular case of k-uniform complete hypergraphs will then be studied. In this framework, we are able to solve typical problems of Rough Set Theory and Formal Concept Analysis using combinatorial techniques. More in detail, we will give a formula to compute the degree of dependency and the partial implication between two sets of attributes, compute the set of reducts and define the structure of the partitions generated by all the definable indiscernibility relations.

Cattaneo, G., Chiaselotti, G., Ciucci, D., & Gentile, T. (2016). On the connection of hypergraph theory with formal concept analysis and rough set theory. INFORMATION SCIENCES, 330, 342-357 [10.1016/j.ins.2015.09.054].

On the connection of hypergraph theory with formal concept analysis and rough set theory

CATTANEO, GIANPIERO
Primo
;
CIUCCI, DAVIDE ELIO
;
2016

Abstract

We present a unique framework for connecting different topics: hypergraphs from one side and Formal Concept Analysis and Rough Set Theory from the other. This is done through the formal equivalence among Boolean information tables, formal contexts and hypergraphs. Links with generic (i.e., not Boolean) information tables are established, through so-called nominal scaling. The particular case of k-uniform complete hypergraphs will then be studied. In this framework, we are able to solve typical problems of Rough Set Theory and Formal Concept Analysis using combinatorial techniques. More in detail, we will give a formula to compute the degree of dependency and the partial implication between two sets of attributes, compute the set of reducts and define the structure of the partitions generated by all the definable indiscernibility relations.
No
Articolo in rivista - Articolo scientifico
Scientifica
Formal concept analysis; Hypergraphs; Rough sets; Artificial Intelligence; Software; Control and Systems Engineering; Theoretical Computer Science; Computer Science Applications1707 Computer Vision and Pattern Recognition; Information Systems and Management
English
342
357
16
Cattaneo, G., Chiaselotti, G., Ciucci, D., & Gentile, T. (2016). On the connection of hypergraph theory with formal concept analysis and rough set theory. INFORMATION SCIENCES, 330, 342-357 [10.1016/j.ins.2015.09.054].
Cattaneo, G; Chiaselotti, G; Ciucci, D; Gentile, T
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/98919
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