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European Conference on Symbolic and Quantitative Approaches with Uncertainty

ECSQARU 2021: Symbolic and Quantitative Approaches to Reasoning with Uncertainty pp 427–441Cite as

Centroids of Credal Sets: A Comparative Study

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12897))

Abstract

We compare a number of different notions of centroid of a credal set: the Shapley value, that arises in the context of game theory; the average of the extreme points; the incenter with respect to the total variation distance between probability measures; and the limit of a procedure of uniform contraction. We show that these four centers do not coincide in general, give some sufficient conditions for their equality, and analyse their axiomatic properties. Finally, we discuss briefly how to define a notion of centrality measure.

Supported by project PGC2018-098623-B-I00. We thank Arthur Van Camp and the anonymous reviewers for some helpful comments and discussion.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, University of Oviedo, Oviedo, Spain

    Enrique Miranda & Ignacio Montes

Authors
  1. Enrique Miranda
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  2. Ignacio Montes
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Correspondence to Enrique Miranda .

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Editors and Affiliations

  1. Institute of Information Theory and Automation, Prague, Czech Republic

    Jiřina Vejnarová

  2. Insight Centre for Data Analytics, School of Computer Science and IT University College Cork, Cork, Ireland

    Nic Wilson

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Miranda, E., Montes, I. (2021). Centroids of Credal Sets: A Comparative Study. In: Vejnarová, J., Wilson, N. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2021. Lecture Notes in Computer Science(), vol 12897. Springer, Cham. https://doi.org/10.1007/978-3-030-86772-0_31

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  • DOI: https://doi.org/10.1007/978-3-030-86772-0_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86771-3

  • Online ISBN: 978-3-030-86772-0

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