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Aggregation Operators on Shadowed Sets Deriving from Conditional Events and Consensus Operators

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Rough Sets (IJCRS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14481))

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Abstract

We introduce particular aggregation operators on shadowed sets, which derive from the operations between conditional events and from the consensus operator. Considering that shadowed sets arise as approximations of fuzzy sets, we also present and study special classes of aggregation functions that can be approximated by the considered operations on shadowed sets.

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Notes

  1. 1.

    We indicate such operations with the symbols \(*_{15}, \ldots , *_{21}\) since other operations \(*_1, \ldots , *_{14}\) are already defined on shadowed sets in [2].

  2. 2.

    The function \(f \otimes g \in [0,1]^X\) is defined as follows: \((f \otimes g)(x)=f(x) \otimes g(x)\) for each \(x \in X\). Similarly, the function \(\mathcal {S}_{(\alpha ,\beta )}(f) * \mathcal {S}_{(\alpha ,\beta )}(g) \in \{0,[0,1],1\}^X\) is defined as follows: \((\mathcal {S}_{(\alpha ,\beta )}(f) * \mathcal {S}_{(\alpha ,\beta )}(g))(x)=\mathcal {S}_{(\alpha ,\beta )}(f)(x) * \mathcal {S}_{(\alpha ,\beta )}(g)(x)\) for each \(x \in X\).

  3. 3.

    \(\otimes _M\) and \(\oplus _M\) are defined as follows: \(x \otimes _M y= \min (x,y)\) and \(x \oplus _M y=\max (x,y)\), for each \(x,y \in [0,1]\) [19].

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Sistemistica e Comunicazione, University of Milano-Bicocca, viale Sarca 336, 20126, Milan, Italy

    Stefania Boffa & Davide Ciucci

  2. IRCCS Ospedale Galeazzi - Sant’Ambrogio, Milan, Italy

    Andrea Campagner

  3. Department of Computer Science, University of Regina, Regina, Canada

    Yiyu Yao

Authors
  1. Stefania Boffa
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  2. Andrea Campagner
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  3. Davide Ciucci
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  4. Yiyu Yao
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Corresponding author

Correspondence to Stefania Boffa .

Editor information

Editors and Affiliations

  1. IRCCS Istituto Ortopedico Galeazzi, Milano, Italy

    Andrea Campagner

  2. Ghent University, Ghent, Belgium

    Oliver Urs Lenz

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Shuyin Xia

  4. University of Warsaw, Warsaw, Poland

    Dominik Ślęzak

  5. AGH University of Science and Technology, Kraków, Poland

    Jarosław Wąs

  6. University of Regina, Regina, SK, Canada

    JingTao Yao

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Boffa, S., Campagner, A., Ciucci, D., Yao, Y. (2023). Aggregation Operators on Shadowed Sets Deriving from Conditional Events and Consensus Operators. In: Campagner, A., Urs Lenz, O., Xia, S., Ślęzak, D., Wąs, J., Yao, J. (eds) Rough Sets. IJCRS 2023. Lecture Notes in Computer Science(), vol 14481. Springer, Cham. https://doi.org/10.1007/978-3-031-50959-9_14

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  • DOI: https://doi.org/10.1007/978-3-031-50959-9_14

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  • Online ISBN: 978-3-031-50959-9

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