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Evidential Top-k Queries Evaluation: Algorithms and Experiments

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Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations (IPMU 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 853))

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Abstract

Top-k queries represent a vigorous tool to rank-order answers and return only the most interesting ones. ETop-k queries were introduced to discriminate answers in the context of evidential databases. Due to their interval degrees, such answers seem to be difficult to rank-order and to interpret. Two methods of ranking intervals were proposed in the evidential context. This paper presents an efficient implementation of these methods and discusses the experimental results obtained.

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Notes

  1. 1.

    Bel and Pl are two functions defined in the object-relational implementation of evidential databases in [5].

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Author information

Authors and Affiliations

  1. LARODEC, Institut Supérieur de Gestion, Université de Tunis, Tunis, Tunisie

    Fatma Ezzahra Bousnina

  2. ESEN, Univ. Manouba, Manouba, Tunisie

    Mouna Chebbah & Mohamed Anis Bach Tobji

  3. LIAS, ENSMA - Université de Poitiers, Poitiers, France

    Fatma Ezzahra Bousnina & Allel Hadjali

  4. Institut des Hautes Etudes Commerciales, Université de Carthage, Tunis, Tunisie

    Boutheina Ben Yaghlane

Authors
  1. Fatma Ezzahra Bousnina
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  2. Mouna Chebbah
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  3. Mohamed Anis Bach Tobji
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  4. Allel Hadjali
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  5. Boutheina Ben Yaghlane
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Corresponding author

Correspondence to Fatma Ezzahra Bousnina .

Editor information

Editors and Affiliations

  1. Universidad de Cádiz, Cádiz, Cadiz, Spain

    Jesús Medina

  2. Universidad de Málaga, Málaga, Málaga, Spain

    Manuel Ojeda-Aciego

  3. Universidad de Granada, Granada, Spain

    José Luis Verdegay

  4. Universidad de Granada, Granada, Spain

    David A. Pelta

  5. Universidad de Málaga, Málaga, Málaga, Spain

    Inma P. Cabrera

  6. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, New York, USA

    Ronald R. Yager

A Appendix

A Appendix

Proof

*Complementarity:

$$\begin{aligned} P(S(R_i) < S(R_j))&= \dfrac{max(0,pl_j - bel_i)- max(0,bel_j - pl_i)}{(pl_i - bel_i) + (pl_j - bel_j)} \end{aligned}$$
$$\begin{aligned} P(S(R_j) < S(R_i))&= \dfrac{max(0,pl_i - bel_j)- max(0,bel_i - pl_j)}{(pl_i - bel_i) + (pl_j - bel_j)} \end{aligned}$$

\(P(S(R_i)< S(R_j))+ P(S(R_j) < S(R_i))\)

$$\begin{aligned}&= \dfrac{max(0,pl_j - bel_i)- max(0,bel_j - pl_i)}{(pl_i - bel_i) + (pl_j - bel_j)}\\&+ \dfrac{max(0,pl_i - bel_j)- max(0,bel_i - pl_j)}{(pl_i - bel_i) + (pl_j - bel_j)}\\&= \dfrac{max(0,pl_j - bel_i)- 0 + max(0,pl_i - bel_j)- 0}{(pl_i - bel_i) + (pl_j - bel_j)}\\&= \dfrac{ pl_j - bel_i + pl_i - bel_j }{ pl_i - bel_i + pl_j - bel_j} = 1 \end{aligned}$$

\(P(S(R_i)< S(R_j))+ P(S(R_j) < S(R_i)) = 1 \)

Property 1

**Transitivity

Let \(S(R_i) = [bel_i;pl_i] \), \(S(R_j) = [bel_j;pl_j]\) and \(S(R_k)= [bel_k;pl_k]\) be three intervals. If \(S(R_i) \succ S(R_j)\) and \( S(R_j) \succ S(R_k)\) then \(S(R_i) \succ S(R_k)\).

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Bousnina, F.E., Chebbah, M., Bach Tobji, M.A., Hadjali, A., Ben Yaghlane, B. (2018). Evidential Top-k Queries Evaluation: Algorithms and Experiments. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_35

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  • DOI: https://doi.org/10.1007/978-3-319-91473-2_35

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  • Online ISBN: 978-3-319-91473-2

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