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On Operations of Restriction and Freezing on Monadic Fuzzy Quantifiers Over Fuzzy Domains

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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))

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Abstract

This article introduces important operations on the class of monadic fuzzy quantifiers, namely, restriction and freezing. These operations are introduced and investigated in the novel frame of monadic fuzzy quantifiers over fuzzy domains.

The second author announces a support of the ERDF/ESF project AI-Met4AI No. CZ.02.1.01/0.0/0.0/17_049/0008414.

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Notes

  1. 1.

    Note that a generalized quantifier is said to be monadic if its arguments are (fuzzy) sets, such as in “Most tigers cannot swim” (type \(\langle 1, 1\rangle \)). Here, the arguments of “most” are a set of tigers and a set of beings that can swim. More complicated are polyadic quantifiers, for which at least one of its arguments is a relation.

  2. 2.

    Note that \(P_{>5}\) is, in accordance with Definition 6, the relativization of \(Q_{>5}\), cf. Theorem 2.

  3. 3.

    More specifically, \((C_{M\cup N}\cup A_{M\cup N})\cap B_{M\cup N} = (C_{M\cup N}\cup A_{M\cup N})\cap (B_{M\cup N}\cap C_{M\cup N})\) does not hold in general; therefore, the fuzzy quantifier Q can assign different values for fuzzy sets \(B_{M\cup N}\) and \((B\cap C)_{M\cup N}\).

References

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Author information

Authors and Affiliations

  1. CE IT4I - IRAFM, University of Ostrava, 30. dubna 22, 701 03, Ostrava, Czech Republic

    Antonín Dvořák & Michal Holčapek

Authors
  1. Antonín Dvořák
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  2. Michal Holčapek
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Corresponding author

Correspondence to Michal Holčapek .

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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Dvořák, A., Holčapek, M. (2022). On Operations of Restriction and Freezing on Monadic Fuzzy Quantifiers Over Fuzzy Domains. 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_56

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_56

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-08971-8

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