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Graduality, Uncertainty and Typicality in Formal Concept Analysis

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35 Years of Fuzzy Set Theory

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 261))

Abstract

There exist several proposals for extending formal concept analysis (FCA) to fuzzy settings. They focus mainly on mathematical aspects and assume generally a residuated algebra in order to maintain the required algebraic properties for the definition of formal concepts. However, less efforts have been devoted for discussing what are the possible reasons for introducing degrees in the relation linking objects and properties (which defines a formal context in the FCA sense), and thus what are the possible meanings of the degrees and how to handle them in agreement with their intended semantics. The paper investigates three different semantics, namely i) the graduality of the link associating properties to objects, pointing out various interpretations of a fuzzy formal context; ii) the uncertainty pervading this link (in case of binary properties) when only imperfect information is available and represented in the framework of possibility theory; and lastly, iii) the typicality of objects and the importance of definitional properties within a class. Remarkably enough, the uncertainty semantics has been hardly considered in the FCA setting, and the third semantics apparently not. Moreover, we provide an algorithm for building the whole fuzzy concept lattice based on Gödel implication for handling gradual properties in a qualitative manner.

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Author information

Authors and Affiliations

  1. University of Tizi-Ouzou, BP 17, RP, 15000, Tizi-Ouzou, Algeria

    Yassine Djouadi

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

    Didier Dubois & Henri Prade

Authors
  1. Yassine Djouadi
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  2. Didier Dubois
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  3. Henri Prade
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Editor information

Editors and Affiliations

  1. Ghent University, Gent, Belgium

    Chris Cornelis , Glad Deschrijver , Mike Nachtegael , Steven Schockaert  & Yun Shi , , ,  & 

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Djouadi, Y., Dubois, D., Prade, H. (2010). Graduality, Uncertainty and Typicality in Formal Concept Analysis. In: Cornelis, C., Deschrijver, G., Nachtegael, M., Schockaert, S., Shi, Y. (eds) 35 Years of Fuzzy Set Theory. Studies in Fuzziness and Soft Computing, vol 261. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16629-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-16629-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16628-0

  • Online ISBN: 978-3-642-16629-7

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