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Logics of Dominance for Reasoning About Multi-criteria Decisions

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 11471))

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Abstract

In this paper, we present modal logics of preference and dominance for reasoning about multi-criteria decisions. We first explore a basic logical framework based on multi-criteria preferences and its special case when the relations are total preorders. Then, we extend the basic formalism to a logic of modal dominances. The syntax, semantics, and complete axiomatization of each logic is presented. Finally, we also consider several extensions and variants of the proposed logics that can represent rules induced by dominance-based rough set analysis and beyond.

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Notes

  1. 1.

    Also called knowledge representation systems, information systems, or attribute-value systems.

  2. 2.

    In the original DRSA, it is also assumed that the relation is total, i.e., it satisfies that, for \(x,y\in V_i\), \(x\succcurlyeq _iy\) or \(y\succcurlyeq _ix\). However, we will model the more general scenario in which there may exist incomparable values. Then, a PODT with all preference relations being total preorders is regarded as a special case.

  3. 3.

    We omit the respective subscripts of \(\preccurlyeq \) and \(\succcurlyeq \) in the rules for brevity.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Penghu University of Science and Technology, Penghu, 880, Taiwan

    Tuan-Fang Fan

  2. Institute of Information Science, Academia Sinica, Taipei, 115, Taiwan

    Churn-Jung Liau

Authors
  1. Tuan-Fang Fan
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  2. Churn-Jung Liau
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Corresponding author

Correspondence to Churn-Jung Liau .

Editor information

Editors and Affiliations

  1. Osaka University, Toyonaka, Osaka, Japan

    Hirosato Seki

  2. Institute for Chemical Research, Kyoto University, Uji, Kyoto, Japan

    Canh Hao Nguyen

  3. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  4. Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

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Fan, TF., Liau, CJ. (2019). Logics of Dominance for Reasoning About Multi-criteria Decisions. In: Seki, H., Nguyen, C., Huynh, VN., Inuiguchi, M. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2019. Lecture Notes in Computer Science(), vol 11471. Springer, Cham. https://doi.org/10.1007/978-3-030-14815-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-14815-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14814-0

  • Online ISBN: 978-3-030-14815-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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