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Cutting of Partial Fuzzy Relations and Their Compositions – The Case of the Dragonfly Operations

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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

Partial fuzzy sets and relations have been recently developed in partial fuzzy set theory to handle undefined values. In this paper, we introduce the definitions of \( \alpha \)-cut and fuzzy \( \alpha \)-cut of partial fuzzy relations. Then some basic properties of these cuts of partial fuzzy relations are addressed. Furthermore, we study numerous properties of the compositions of \( \alpha \)-cut or fuzzy \( \alpha \)-cut of partial fuzzy relations. Additionally, we focus on the relationship between the compositions of the cuts of partial fuzzy relations on the one hand side, and the cuts of the compositions of the partial fuzzy relations on the other side.

The authors announce the support of Czech Science Foundation through the grant 20-07851S, and the partial support from ERDF/ESF project CZ.02.1.01/0.0/0.0/17-049/0008414.

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Authors and Affiliations

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

    Nhung Cao & Martin Štěpnička

Authors
  1. Nhung Cao
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  2. Martin Štěpnička
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Correspondence to Martin Štěpnička .

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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Cao, N., Štěpnička, M. (2022). Cutting of Partial Fuzzy Relations and Their Compositions – The Case of the Dragonfly Operations. 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_54

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  • DOI: https://doi.org/10.1007/978-3-031-08971-8_54

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  • Online ISBN: 978-3-031-08971-8

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