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Decision-Aid Methods Based on Belief Function Theory with Application to Torrent Protection

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Information Quality in Information Fusion and Decision Making

Part of the book series: Information Fusion and Data Science ((IFDS))

Abstract

In mountainous areas, decision-makers must find the best solution to protect elements-at-torrential risk. The decision process involves several criteria and is based on imperfect information. Classical Multi-Criteria Decision-Aiding methods (MCDAs) are restricted to precise criteria evaluation for decision-making under a risky environment and suffer of rank reversal problems. To bridge these gaps, several MCDAs have been recently developed within belief function theory framework. The aims of this chapter are to introduce how these methods can be applied in practice and to introduce their general principles. To show their applicability to the real-life problem, we apply them to the Decision-Making Problem (DMP) comprising the comparison of several protective alternatives against torrential floods and selection of the most efficient one. We finally discuss the method improvements to promote their practical implementation.

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Notes

  1. 1.

    Indeed, the ignorance of a parameter value x belonging to [a, b] is usually modeled by a uniform probability distribution function (pdf) over [a, b], which yields from the probability calculus to a nonuniform pdf of 1∕x on [1∕b; 1∕a]. This result is not acceptable from the ignorance modeling standpoint because if one has no specific information on x, we cannot get more information on 1∕x but that 1∕x belongs to [1∕b; 1∕a]. Therefore the uniform pdf often used to model ignorance in probability theory is problematic.

  2. 2.

    For a technical reason, one allows to commit some mass on the empty set in this discounting. This is not a problem because the final fusion result will be normalized.

  3. 3.

    For any BBAs x, y, z defined on 2Θ, a true distance metric d(x, y) satisfies the properties of non-negativity (d(x, y) ≥ 0), non-degeneracy (d(x, y) = 0 ⇔ x = y), symmetry (d(x, y) = d(y, x)), and triangle inequality (d(x, y) + d(y, z) ≥ d(x, z)).

  4. 4.

    Q l = liquid flow.

  5. 5.

    V s = solid volume.

  6. 6.

    V l = debris flow volume.

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Acknowledgements

This study was partially funded by the French Agricultural and Forest Ministry (MAA) and the French Environment Ministry (MTES).

Author information

Authors and Affiliations

  1. Département Risques Naturels (DRN), Office National des Forêts (ONF), Grenoble, France

    Simon Carladous

  2. Snow Avalanche Engineering and Torrent Control Research Unit (ETNA), Université Grenoble Alpes, Irstea – UR ETGR, St-Martin d’Hères Cedex, France

    Jean-Marc Tacnet

  3. ONERA, The French Aerospace Lab, Palaiseau Cedex, France

    Jean Dezert

  4. Institut Henri Fayol, UMR LIMOS 6158, Ecole Nationale Supérieure des Mines de Saint-Etienne, Saint-Etienne Cedex 2, France

    Mireille Batton-Hubert

Authors
  1. Simon Carladous
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  2. Jean-Marc Tacnet
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  4. Mireille Batton-Hubert
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Corresponding author

Correspondence to Simon Carladous .

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Editors and Affiliations

  1. IMT-Atlantique, Brest, France

    Éloi Bossé

  2. The State University of New York at Buffalo, Buffalo, NY, USA

    Galina L. Rogova

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Carladous, S., Tacnet, JM., Dezert, J., Batton-Hubert, M. (2019). Decision-Aid Methods Based on Belief Function Theory with Application to Torrent Protection. In: Bossé, É., Rogova, G. (eds) Information Quality in Information Fusion and Decision Making. Information Fusion and Data Science. Springer, Cham. https://doi.org/10.1007/978-3-030-03643-0_15

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  • DOI: https://doi.org/10.1007/978-3-030-03643-0_15

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  • Online ISBN: 978-3-030-03643-0

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