Asymmetric Composition of Possibilistic Operators in Formal Concept Analysis: Application to the Extraction of Attribute Implications from Incomplete Contexts.

Zina Ait-Yakoub (1) , Yassine Djouadi (2) , Didier Dubois (3, 4) , Henri Prade (3, 4)

1 UMMTO - Université Mouloud Mammeri [Tizi Ouzou]
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]
3 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
4 CNRS - Centre National de la Recherche Scientifique

Formal concept analysis theory (FCA) classically relies on the use of the Galois powerset operator. Formal similarities between possibility theory and formal concept analysis have led to the use of possibilistic operators in FCA, which were ignored before. In this paper, an approach based on the use of asymmetric composition of the two most usual possibilistic operators is proposed. It enables us to complement the stem base, by deriving attribute implications with disjunctions on both sides of the implications. Besides, the approach is also generalized to incomplete contexts involving explicit positive and negative information. We outline the potential application of these results to the completion of TBoxes in description logic.

Mots clés: Formal concept analysis (FCA); Galois derivation operator; TBoxes; Asymmetric composition

Domaines: Logique en informatique [cs.LO]

Zina Ait-Yakoub, Yassine Djouadi, Didier Dubois, Henri Prade. Asymmetric Composition of Possibilistic Operators in Formal Concept Analysis: Application to the Extraction of Attribute Implications from Incomplete Contexts.. International Journal of Intelligent Systems, 2017, 32 (12), pp.1285-1311. ⟨10.1002/int.21900⟩. ⟨hal-02552195⟩