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Comparing Hexagons of Opposition in Probabilistic Rough Set Theory

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1601))

Abstract

A hexagon of opposition built from a probabilistic rough set depends on two thresholds. This work explores the relations of opposition among vertices of hexagons obtained from pairs of thresholds. By an exhaustive analysis of the different cases that can arise, twelve patterns are defined and studied.

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Notes

  1. 1.

    If \(\alpha < \alpha '\), then \(P_{NEG \cup BND}\) and \(P_{POS'}\) are contraries by Theorem 4, and \(P_{NEG' \cup BND'}\) and \(P_{POS}\) are sub-contraries by Theorem 5.

  2. 2.

    If \(\beta < \beta '\), then \(P_{POS \cup BND}\) and \(P_{NEG'}\) are contraries by Theorem 4, and \(P_{POS' \cup BND'}\) and \(P_{NEG}\) are sub-contraries by Theorem 5.

  3. 3.

    If \(\beta < \alpha '\), then \(P_{POS'}\) and \(P_{NEG}\) are contraries by Theorem 15.

  4. 4.

    If \(\beta < \alpha '\), then \(P_{POS \cup BND}\) and \(P_{NEG' \cup BND'}\) are sub-contraries by Theorem 16.

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Authors and Affiliations

  1. DISCo, Università degli Studi di Milano-Bicocca, Viale Sarca 336, 20126, Milano, Italy

    Stefania Boffa & Davide Ciucci

  2. NSC IT4Innovations, Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Petra Murinová

Authors
  1. Stefania Boffa
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  2. Davide Ciucci
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  3. Petra Murinová
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Corresponding author

Correspondence to Stefania Boffa .

Editor information

Editors and Affiliations

  1. University of Milano-Bicocca, Milan, Italy

    Davide Ciucci

  2. University of Oviedo, Oviedo, Spain

    Inés Couso

  3. University of Cádiz, Cádiz, Spain

    Jesús Medina

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. University of Perugia, Perugia, Italy

    Davide Petturiti

  6. Sorbonne Université, Paris, France

    Bernadette Bouchon-Meunier

  7. Iona College, New Rochelle, NY, USA

    Ronald R. Yager

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Boffa, S., Ciucci, D., Murinová, P. (2022). Comparing Hexagons of Opposition in Probabilistic Rough Set Theory. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_51

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_51

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