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Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings

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Scalable Uncertainty Management (SUM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11142))

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Abstract

Mainstream approaches to uncertainty modeling in relational databases are probabilistic. Still some researchers persist in proposing representations based on possibility theory. They are motivated by the ability of this latter setting for modeling epistemic uncertainty and by its qualitative nature. Interestingly enough, several possibilistic models have been proposed over time, and have been motivated by different application needs ranging from database querying, to database design and to data cleaning. Thus, one may distinguish between four different frameworks ordered here according to an increasing representation power: databases with (i) layered tuples; (ii) certainty-qualified attribute values; (iii) attribute values restricted by general possibility distributions; (iv) possibilistic c-tables. In each case, we discuss the role of the possibility-necessity duality, the limitations and the benefit of the representation settings, and their suitability with respect to different tasks.

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Notes

  1. 1.

    Then the attribute value, or more generally the disjunction of possible values is/are considered as fully possible, while any other value in the attribute domain is all the less possible as the certainty level is higher. In case of full certainty these other values are all impossible. This is a particular case of the certainty qualification of a fuzzy set, here reduced to a singleton, or in any case to a classical subset. There are other basic qualifications of a fuzzy set in possibility theory, for instance in terms of guaranteed possibility (rather than in terms of necessity as in certainty qualification), or which lead to enlarge the core, or to reduce the support of the fuzzy set, see [7] for the four canonic transformations; see also [20] for hybrid transformations combining enlargement with uncertainty.

  2. 2.

    For example, assume Peter has two ages, each with a certainty level, the levels being denoted by \(\alpha \) and \(\beta \) respectively. Then the FD name \(\rightarrow \) age is violated with a certainty degree that is equal to \(\min (\alpha ,\,\beta )\).

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Author information

Authors and Affiliations

  1. ENSSAT-Lannion, IRISA, Rennes, France

    Olivier Pivert

  2. IRIT – CNRS, 118, route de Narbonne, 31062 , Toulouse Cedex 09, France

    Henri Prade

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  1. Olivier Pivert
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Correspondence to Olivier Pivert .

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Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Milano-Bicocca, Milan, Italy

    Gabriella Pasi

  3. Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

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Pivert, O., Prade, H. (2018). Handling Uncertainty in Relational Databases with Possibility Theory - A Survey of Different Modelings. In: Ciucci, D., Pasi, G., Vantaggi, B. (eds) Scalable Uncertainty Management. SUM 2018. Lecture Notes in Computer Science(), vol 11142. Springer, Cham. https://doi.org/10.1007/978-3-030-00461-3_30

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  • DOI: https://doi.org/10.1007/978-3-030-00461-3_30

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