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Formal Concept Analysis from the Standpoint of Possibility Theory

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Formal Concept Analysis (ICFCA 2015)

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Abstract

Formal concept analysis (FCA) and possibility theory (PoTh) have been developed independently. They address different concerns in information processing: while FCA exploits relations linking objects and properties, and has applications in data mining and clustering, PoTh deals with the modeling of (graded) epistemic uncertainty. However, making a formal parallel between FCA and PoTh is fruitful. The four set-functions at work in PoTh have meaningful counterparts in FCA; this leads to consider operators neglected in FCA, and thus new fixed point equations. One of these pairs of equations, paralleling the one defining formal concepts in FCA, defines independent sub-contexts of objects and properties that have nothing in common. The similarity of the structures underlying FCA and PoTh is still more striking, using a cube of opposition (a device extending the traditional square of opposition in logic). Beyond the parallel between FCA and PoTh, this invited contribution, which largely relies on several past publications by the authors, also addresses issues pertaining to the possible meanings, degree of satisfaction vs. degree of certainty, of graded object-property links, which calls for distinct manners of handling the degrees. Other lines of interest for further research are briefly mentioned.

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Notes

  1. 1.

    We again provide the proof for the sake of self-containedness.

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Authors and Affiliations

  1. IRIT, Université Paul Sabatier, 118 Route de Narbonne, 31062, Toulouse Cedex 09, France

    Didier Dubois & Henri Prade

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  1. Didier Dubois
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  2. Henri Prade
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Correspondence to Henri Prade .

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Editors and Affiliations

  1. Universitat Politècnica de Catalunya, Barcelona, Spain

    Jaume Baixeries

  2. Babeş-Bolyai University, Cluj-Napoca, Romania

    Christian Sacarea

  3. Departamento de Matemática Aplicada, Universidad de Málaga, Malaga, Spain

    Manuel Ojeda-Aciego

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Dubois, D., Prade, H. (2015). Formal Concept Analysis from the Standpoint of Possibility Theory. In: Baixeries, J., Sacarea, C., Ojeda-Aciego, M. (eds) Formal Concept Analysis. ICFCA 2015. Lecture Notes in Computer Science(), vol 9113. Springer, Cham. https://doi.org/10.1007/978-3-319-19545-2_2

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  • DOI: https://doi.org/10.1007/978-3-319-19545-2_2

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